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The eccentricity of the hyperbola with asymptotes 3x + 4y = 2 and 4x – 3y = 2 is

3
2
$\sqrt{2}$ $\sqrt{2}$
4

hint Hint:

The eccentricity of a hyperbola is always greater than 1. i.e. e > 1. The eccentricity of a hyperbola can be taken as the ratio of the distance of the point on the hyperbole, from the focus, and its distance from the directrix.
Eccentricity = Distance from Focus/Distance from Directrix

The correct answer is: $square root of 2$
$square root of 2$

We have been given two asymptotes i.e. 3x + 4y = 2 and 4x – 3y = 2
First find out their slopes
$m 1 space equals negative space 3 over 4 space a n d space m 2 space equals space 4 over 3$
From above we can see that m1 and m2 are negative inverse of each other that means both are perpendicular to each other.
It is a rectangular hyperbola and it has fixed eccentricity.
Thus eccentricity = $square root of 2$

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

Maths-General

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physics

Which area shows the displacement covered by the particle after time t.

physicsGeneral

General

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Polarization power of a cation increases when

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

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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

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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

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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

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

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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

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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?

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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 -

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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....

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The eccentricity of the hyperbola with asymptotes 3x + 4y = 2 and 4x – 3y = 2 is

3 2 4

The eccentricity of a hyperbola is always greater than 1. i.e. e > 1. The eccentricity of a hyperbola can be taken as the ratio of the distance of the point on the hyperbole, from the focus, and its distance from the directrix.Eccentricity = Distance from Focus/Distance from Directrix

The correct answer is:

We have been given two asymptotes i.e. 3x + 4y = 2 and 4x – 3y = 2First find out their slopesFrom above we can see that m1 and m2 are negative inverse of each other that means both are perpendicular to each other.It is a rectangular hyperbola and it has fixed eccentricity.Thus eccentricity =

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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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3
2
$\sqrt{2}$ $\sqrt{2}$
4

The eccentricity of a hyperbola is always greater than 1. i.e. e > 1. The eccentricity of a hyperbola can be taken as the ratio of the distance of the point on the hyperbole, from the focus, and its distance from the directrix.
Eccentricity = Distance from Focus/Distance from Directrix

The correct answer is: $square root of 2$
$square root of 2$

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....