If the curve x2 + 3y2 = 9 subtends an obtuse angle at the point-Turito

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General

Easy

Botany-

If the curve x² + 3y² = 9 subtends an obtuse angle at the point (2a, a), then a possible value of a² is

Botany-General

1
2
3
4

Answer:The correct answer is: 2The given curve is , whose director circle is x² + y² = 12. For the required condition (2a, a) should lie inside the circle and outside the ellipse i.e.,(2a)² + 3a² - 9 > 0 and (2a)² + a² - 12 < 0 i.e., .

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Related Questions to study

General

botany-

If the tangent at Point P to the ellipse 16x² + 11y² = 256 is also the tangent to the circle x² + y² - 2x = 15, then the eccentric angle of point P is

The equation of tangent at point

to the ellipse
16x² + 11y² = 256 is
16x (4cosq) + 11y

= 256
4xcosq +

y sinq = 16
This touches the circle
(x + 1)² + y² = 16
So,

= 4
Þ (cosq - 4)² = 11 + 5cos²q
4cos²q + 8cosq - 5 = 0
\ cosq =

\ q = ±

If the tangent at Point P to the ellipse 16x² + 11y² = 256 is also the tangent to the circle x² + y² - 2x = 15, then the eccentric angle of point P is

botany-General

The equation of tangent at point

to the ellipse
16x² + 11y² = 256 is
16x (4cosq) + 11y

= 256
4xcosq +

y sinq = 16
This touches the circle
(x + 1)² + y² = 16
So,

= 4
Þ (cosq - 4)² = 11 + 5cos²q
4cos²q + 8cosq - 5 = 0
\ cosq =

\ q = ±

General

botany-

From the focus $left parenthesis negative 5 , 0 right parenthesis$ of the ellipse $fraction numerator x to the power of 2 end exponent over denominator 45 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 20 end fraction equals 1$ a ray of light is sent which makes angle $c o s to the power of negative 1 end exponent invisible function application open parentheses fraction numerator negative 1 over denominator square root of 5 end fraction close parentheses$ with the positive direction of X-axis upon reacting the ellipse the ray is reflected from it. Slope of the reflected ray is

Let

Foci are

Equation of line through (-5, 0) with slope –2 is

This line meets the ellipse above X-axis at

Slope =

.

From the focus $left parenthesis negative 5 , 0 right parenthesis$ of the ellipse $fraction numerator x to the power of 2 end exponent over denominator 45 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 20 end fraction equals 1$ a ray of light is sent which makes angle $c o s to the power of negative 1 end exponent invisible function application open parentheses fraction numerator negative 1 over denominator square root of 5 end fraction close parentheses$ with the positive direction of X-axis upon reacting the ellipse the ray is reflected from it. Slope of the reflected ray is

botany-General

Let

Foci are

Equation of line through (-5, 0) with slope –2 is

This line meets the ellipse above X-axis at

If $f left parenthesis x right parenthesis$ is a decreasing function for all $x element of R$ and $f left parenthesis x right parenthesis greater than 0 for all x element of R$ then the range of K so that the equation $fraction numerator x to the power of 2 end exponent over denominator f open parentheses K to the power of 2 end exponent plus 2 K plus 5 close parentheses end fraction plus fraction numerator y to the power of 2 end exponent over denominator f left parenthesis K plus 11 right parenthesis end fraction equals 1$ represents an ellipse whose major axis is the X-axis is

Conceptual

If $f left parenthesis x right parenthesis$ is a decreasing function for all $x element of R$ and $f left parenthesis x right parenthesis greater than 0 for all x element of R$ then the range of K so that the equation $fraction numerator x to the power of 2 end exponent over denominator f open parentheses K to the power of 2 end exponent plus 2 K plus 5 close parentheses end fraction plus fraction numerator y to the power of 2 end exponent over denominator f left parenthesis K plus 11 right parenthesis end fraction equals 1$ represents an ellipse whose major axis is the X-axis is

$P comma Q blank$ are points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1$ such that $P Q$ is a chord through the point $R left parenthesis 3 , 0 right parenthesis text . end text$ If $vertical line P R vertical line equals 2$ then length of chord $P Q$ is

Conceptual

$P comma Q blank$ are points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1$ such that $P Q$ is a chord through the point $R left parenthesis 3 , 0 right parenthesis text . end text$ If $vertical line P R vertical line equals 2$ then length of chord $P Q$ is

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 7 , 3 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

P lies on the ellipse for which

are foci and length of major axis is 10 and eccentricity is 3/5.

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 7 , 3 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

botany-General

P lies on the ellipse for which

are foci and length of major axis is 10 and eccentricity is 3/5.

General

botany-

If the curve $x to the power of 2 end exponent plus 3 y to the power of 2 end exponent equals 9$ subtends as obtuse angle at the point $left parenthesis 2 alpha comma alpha right parenthesis left parenthesis left parenthesis alpha element of text int end text text eger end text text end text right parenthesis$ , $blank left parenthesis alpha element of text int eger end text right parenthesis$ then a possible value of is

The generated curve is

, whose director circle is

. For the required condition

should lie inside the circle and out side the ellipse i.e.

If the curve $x to the power of 2 end exponent plus 3 y to the power of 2 end exponent equals 9$ subtends as obtuse angle at the point $left parenthesis 2 alpha comma alpha right parenthesis left parenthesis left parenthesis alpha element of text int end text text eger end text text end text right parenthesis$ , $blank left parenthesis alpha element of text int eger end text right parenthesis$ then a possible value of is

botany-General

The generated curve is

, whose director circle is

. For the required condition

should lie inside the circle and out side the ellipse i.e.

General

botany-

Tangent at any point of ellipse $9 x to the power of 2 end exponent plus 16 y to the power of 2 end exponent minus 144 equals 0$ is drawn. Eccentric
angle of ‘ P’ is $theta equals fraction numerator 1 over denominator 2 end fraction s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 7 end fraction close parentheses$ If is the foot of perpendicular from centre $blank ´ O blank ´$ to this tangent then $angle P O N$ is

botany-General

General

botany-

If there are exactly two points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ whose distance from its centre is same and is equal to $square root of fraction numerator a to the power of 2 end exponent plus 2 b to the power of 2 end exponent over denominator 2 end fraction end root$ then eccentricity of the ellipse is

botany-General

General

botany-

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

…. (1)

… (2)

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

The protective covering over radical during the germination of seeds is

biologyGeneral

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maths-

The domain of the function $f left parenthesis x right parenthesis equals l o g subscript 10 end subscript invisible function application left parenthesis square root of x minus 4 end root plus square root of 6 minus x end root right parenthesis$ is

maths-General

General

biology

Alkaline pyrogallic acid is used for absorbing _______ during experiments on germination

biologyGeneral

General

physics

The maximum speed with which a car can cross a convex bridge over a river with radius of curvature 9 m is : (given that the centre of gravity of car is 1m above the road)-

physicsGeneral

General

physics

The roadway of a bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motor cycle can cross the bridge without leaving ground.

physicsGeneral

General

physics

2 kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m /sec. The tension in the string will be 52 N when the stone is-

physicsGeneral

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

If the curve x² + 3y² = 9 subtends an obtuse angle at the point (2a, a), then a possible value of a² is

1
2
3
4

Answer:The correct answer is: 2The given curve is , whose director circle is x² + y² = 12. For the required condition (2a, a) should lie inside the circle and outside the ellipse i.e.,(2a)² + 3a² - 9 > 0 and (2a)² + a² - 12 < 0 i.e., .

Book A Free Demo

Related Questions to study

If the tangent at Point P to the ellipse 16x² + 11y² = 256 is also the tangent to the circle x² + y² - 2x = 15, then the eccentric angle of point P is

If the tangent at Point P to the ellipse 16x² + 11y² = 256 is also the tangent to the circle x² + y² - 2x = 15, then the eccentric angle of point P is

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 7 , 3 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 7 , 3 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

The protective covering over radical during the germination of seeds is

The protective covering over radical during the germination of seeds is

The domain of the function $f left parenthesis x right parenthesis equals l o g subscript 10 end subscript invisible function application left parenthesis square root of x minus 4 end root plus square root of 6 minus x end root right parenthesis$ is

The domain of the function $f left parenthesis x right parenthesis equals l o g subscript 10 end subscript invisible function application left parenthesis square root of x minus 4 end root plus square root of 6 minus x end root right parenthesis$ is

Alkaline pyrogallic acid is used for absorbing _______ during experiments on germination

Alkaline pyrogallic acid is used for absorbing _______ during experiments on germination

The maximum speed with which a car can cross a convex bridge over a river with radius of curvature 9 m is : (given that the centre of gravity of car is 1m above the road)-

The maximum speed with which a car can cross a convex bridge over a river with radius of curvature 9 m is : (given that the centre of gravity of car is 1m above the road)-

The roadway of a bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motor cycle can cross the bridge without leaving ground.

The roadway of a bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motor cycle can cross the bridge without leaving ground.

2 kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m /sec. The tension in the string will be 52 N when the stone is-

2 kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m /sec. The tension in the string will be 52 N when the stone is-

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Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

If the curve x2 + 3y2 = 9 subtends an obtuse angle at the point (2a, a), then a possible value of a2 is

1 2 3 4

Answer:The correct answer is: 2The given curve is , whose director circle is x2 + y2 = 12. For the required condition (2a, a) should lie inside the circle and outside the ellipse i.e.,(2a)2 + 3a2 - 9 > 0 and (2a)2 + a2 - 12 < 0 i.e., .

Book A Free Demo

Related Questions to study

If the tangent at Point P to the ellipse 16x2 + 11y2 = 256 is also the tangent to the circle x2 + y2 - 2x = 15, then the eccentric angle of point P is

If the tangent at Point P to the ellipse 16x2 + 11y2 = 256 is also the tangent to the circle x2 + y2 - 2x = 15, then the eccentric angle of point P is

From the focus of the ellipse a ray of light is sent which makes angle with the positive direction of X-axis upon reacting the ellipse the ray is reflected from it. Slope of the reflected ray is

From the focus of the ellipse a ray of light is sent which makes angle with the positive direction of X-axis upon reacting the ellipse the ray is reflected from it. Slope of the reflected ray is

If is a decreasing function for all and then the range of K so that the equation represents an ellipse whose major axis is the X-axis is

If is a decreasing function for all and then the range of K so that the equation represents an ellipse whose major axis is the X-axis is

are points on the ellipse such that is a chord through the point If then length of chord is

are points on the ellipse such that is a chord through the point If then length of chord is

Let . A point P in the XY-plane varies in such a way that perimeter of is 16. Then the maximum area of is

Let . A point P in the XY-plane varies in such a way that perimeter of is 16. Then the maximum area of is

If the curve subtends as obtuse angle at the point , then a possible value of is

If the curve subtends as obtuse angle at the point , then a possible value of is

Tangent at any point of ellipse is drawn. Eccentricangle of ‘ P’ is If is the foot of perpendicular from centre to this tangent then is

Tangent at any point of ellipse is drawn. Eccentricangle of ‘ P’ is If is the foot of perpendicular from centre to this tangent then is

If there are exactly two points on the ellipse whose distance from its centre is same and is equal to then eccentricity of the ellipse is

If there are exactly two points on the ellipse whose distance from its centre is same and is equal to then eccentricity of the ellipse is

An ellipse slides between two perpendicular straight lines then, locus of its foci is

An ellipse slides between two perpendicular straight lines then, locus of its foci is

The protective covering over radical during the germination of seeds is

The protective covering over radical during the germination of seeds is

The domain of the function is

The domain of the function is

Alkaline pyrogallic acid is used for absorbing _______ during experiments on germination

Alkaline pyrogallic acid is used for absorbing _______ during experiments on germination

The maximum speed with which a car can cross a convex bridge over a river with radius of curvature 9 m is : (given that the centre of gravity of car is 1m above the road)-

The maximum speed with which a car can cross a convex bridge over a river with radius of curvature 9 m is : (given that the centre of gravity of car is 1m above the road)-

The roadway of a bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motor cycle can cross the bridge without leaving ground.

The roadway of a bridge over a canal is in the form of a circular arc of radius 18 m. What is the greatest speed with which a motor cycle can cross the bridge without leaving ground.

2 kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m /sec. The tension in the string will be 52 N when the stone is-

2 kg stone at the end of a string 1m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m /sec. The tension in the string will be 52 N when the stone is-

Courses

Quick Links

If the curve x² + 3y² = 9 subtends an obtuse angle at the point (2a, a), then a possible value of a² is

1
2
3
4

Answer:The correct answer is: 2The given curve is , whose director circle is x² + y² = 12. For the required condition (2a, a) should lie inside the circle and outside the ellipse i.e.,(2a)² + 3a² - 9 > 0 and (2a)² + a² - 12 < 0 i.e., .

If the tangent at Point P to the ellipse 16x² + 11y² = 256 is also the tangent to the circle x² + y² - 2x = 15, then the eccentric angle of point P is

If the tangent at Point P to the ellipse 16x² + 11y² = 256 is also the tangent to the circle x² + y² - 2x = 15, then the eccentric angle of point P is

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 7 , 3 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 7 , 3 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

An ellipse slides between two perpendicular straight lines $x equals 0 blank a n d blank Y equals 0$ then, locus of its foci is

The domain of the function $f left parenthesis x right parenthesis equals l o g subscript 10 end subscript invisible function application left parenthesis square root of x minus 4 end root plus square root of 6 minus x end root right parenthesis$ is

The domain of the function $f left parenthesis x right parenthesis equals l o g subscript 10 end subscript invisible function application left parenthesis square root of x minus 4 end root plus square root of 6 minus x end root right parenthesis$ is