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The equation of the ellipse with axes along the x – axis and the y – axis, which passes through the points P (4, 3) and Q (6, 2) is

$\frac{x^{2}}{50} + \frac{y^{2}}{13} = 1$
$\frac{x^{2}}{52} + \frac{y^{2}}{13} = 1$
$\frac{x^{2}}{13} + \frac{y^{2}}{52} = 1$
$\frac{x^{2}}{52} + \frac{y^{2}}{17} = 1$

hint Hint:

When the centre of the ellipse is at the origin (0,0) and the foci are on the x-axis and y-axis, then we can easily derive the ellipse equation.
The equation of the ellipse is given by;
$x squared over a squared plus y squared over b squared space equals space 1$

The correct answer is: $fraction numerator x to the power of 2 end exponent over denominator 52 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 13 end fraction equals 1$

The equation of the ellipse is given by;
$x squared over a squared plus y squared over b squared space equals space 1$ ........ (1)
Given : It passes through the points P (4, 3) and Q (6, 2)
Thus from equation (1)
$16 over a squared plus 9 over b squared space equals space 1$ ........... (a)
$36 over a squared plus 4 over b squared space equals space 1$ ........... (b)
Subtracting (b) from (a), we get
$fraction numerator negative 20 over denominator a squared end fraction plus 5 over b squared space equals space 0 5 a squared space equals space 20 b squared a squared space equals space 4 b squared$

Putting the value of $a squared$ in equation (a)
$fraction numerator 16 over denominator 4 b squared end fraction plus 9 over b squared space equals space 1 b squared space equals space 13 a squared space equals space 4 b squared space equals space 4 space cross times 13 space equals space 52 T h u s comma space e q u a t i o n space o f space e l l i p s e space equals space x squared over 52 plus space y squared over 13 space equals space 1$

The number of values of c such that st. line y = 4x + c touches the curve $fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus y to the power of 2 end exponent equals 1$ is

Maths-General

General

Maths-

Tangents are drawn to the ellipse $fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1$ at the ends of the latus rectum. The are of the quadrilateral so formed is

Maths-General

General

Maths-

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

Maths-General

General

physics

Here are the graphs of x→ t of moving body. which of them is not suitable?

physicsGeneral

General

Maths-

A cubic polynomial f(x) = ax³ + bx² + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

If a function has a tangent at a point $x = a$ , then, it means, it is the critical point of that function and the derivative of the function is zero at that point.
Perform the calculations carefully, to avoid silly mistakes.
One should know how to read a graph to solve such questions.

A cubic polynomial f(x) = ax³ + bx² + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

Maths-General

General

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Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b $sin invisible function application fraction numerator pi over denominator 2 end fraction x$ , 1 £ x £ 2 then which of the following is correct?

Maths-General

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The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval $open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction close square brackets$ is -

Maths-General

General

physics

The relation between time and displacement of a moving particle is given by $t equals 2 a x squared$ where $alpha$ is a constant. The shape of the graph is $x not stretchy rightwards arrow y$ is....

physicsGeneral

General

Maths-

If P (q) and Q $open parentheses fraction numerator pi over denominator 2 end fraction plus theta close parentheses$ are two points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , then locus of the mid – point of PQ is

Maths-General

General

Maths-

If CP and CD are semi – conjugate diameters of an ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1 comma$ then CP² + CD² =

Maths-General

General

Maths-

The normals to the curve x = a ( $theta$ + sin $theta$ ), y = a (1 – cos $theta$ ) at the points $theta$ = (2n + 1) $pi$ , n $element of$ I are all -

Maths-General

General

Maths-

The normal to the curve x = 3 cos $theta$ – cos3 $theta$ , y = 3 sin $theta$ – sin3 $theta$ at the point $theta$ = $pi$ /4 passes through the point -

Maths-General

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The equation of the ellipse with axes along the x – axis and the y – axis, which passes through the points P (4, 3) and Q (6, 2) is

When the centre of the ellipse is at the origin (0,0) and the foci are on the x-axis and y-axis, then we can easily derive the ellipse equation.The equation of the ellipse is given by;

The correct answer is:

The equation of the ellipse is given by; ........ (1) Given : It passes through the points P (4, 3) and Q (6, 2) Thus from equation (1) ........... (a) ........... (b)Subtracting (b) from (a), we getPutting the value of in equation (a)

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Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b , 1 £ x £ 2 then which of the following is correct?

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The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval is -

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The normals to the curve x = a ( + sin ), y = a (1 – cos ) at the points = (2n + 1) , n I are all -

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When the centre of the ellipse is at the origin (0,0) and the foci are on the x-axis and y-axis, then we can easily derive the ellipse equation.
The equation of the ellipse is given by;
$x squared over a squared plus y squared over b squared space equals space 1$

The correct answer is: $fraction numerator x to the power of 2 end exponent over denominator 52 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 13 end fraction equals 1$

The number of values of c such that st. line y = 4x + c touches the curve $fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus y to the power of 2 end exponent equals 1$ is

The number of values of c such that st. line y = 4x + c touches the curve $fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus y to the power of 2 end exponent equals 1$ is

Tangents are drawn to the ellipse $fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1$ at the ends of the latus rectum. The are of the quadrilateral so formed is

Tangents are drawn to the ellipse $fraction numerator x to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1$ at the ends of the latus rectum. The are of the quadrilateral so formed is

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

A cubic polynomial f(x) = ax³ + bx² + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

A cubic polynomial f(x) = ax³ + bx² + cx + d has a graph which touches the x-axis at 2, has another x-intercept at –1 and has y-intercept at –2 as shown. The value of, a + b + c + d equals

Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b $sin invisible function application fraction numerator pi over denominator 2 end fraction x$ , 1 £ x £ 2 then which of the following is correct?

Consider f(x) = |1–x| 1 £ x £ 2 and g(x )= f(x) + b $sin invisible function application fraction numerator pi over denominator 2 end fraction x$ , 1 £ x £ 2 then which of the following is correct?

The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval $open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction close square brackets$ is -

The value of c in Lagrange’s theorem for the function f(x) = log sin x in the interval $open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator 5 pi over denominator 6 end fraction close square brackets$ is -

The relation between time and displacement of a moving particle is given by $t equals 2 a x squared$ where $alpha$ is a constant. The shape of the graph is $x not stretchy rightwards arrow y$ is....

The relation between time and displacement of a moving particle is given by $t equals 2 a x squared$ where $alpha$ is a constant. The shape of the graph is $x not stretchy rightwards arrow y$ is....

The normals to the curve x = a ( $theta$ + sin $theta$ ), y = a (1 – cos $theta$ ) at the points $theta$ = (2n + 1) $pi$ , n $element of$ I are all -

The normals to the curve x = a ( $theta$ + sin $theta$ ), y = a (1 – cos $theta$ ) at the points $theta$ = (2n + 1) $pi$ , n $element of$ I are all -

The normal to the curve x = 3 cos $theta$ – cos3 $theta$ , y = 3 sin $theta$ – sin3 $theta$ at the point $theta$ = $pi$ /4 passes through the point -

The normal to the curve x = 3 cos $theta$ – cos3 $theta$ , y = 3 sin $theta$ – sin3 $theta$ at the point $theta$ = $pi$ /4 passes through the point -