Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 3

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JEE Main/Advanced

IMPORTANT

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The condition that a straight line with slope $m$ will be normal to parabola, $y^{2} = 4 a x$ as well as a tangent to rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is

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Important Questions on Hyperbola

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 4

The equation to the common tangents to the two hyperbolas

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

and

\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1

are

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 5

If the foci of the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{b^{2}} = 1

and the hyperbola

\frac{x^{2}}{144} - \frac{y^{2}}{81} = \frac{1}{25}

coincide, then the value of

b^{2}

is:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 6

If

P Q

is a double ordinate of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

such that

O P Q

is an equilateral triangle

O

being the centre of the hyperbola. Then, the eccentricity

e

of the hyperbola satisfies

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 7

Consider the set of hyperbola

x y = k, k \in R

. Let

e_{1}

be the eccentricity when

k = 4

and

e_{2}

be the eccentricity when

k = 9

then

e_{1} - e_{2} =

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 8

Equation of the hyperbola passing through the point

(1, - 1)

and having asymptotes

x + 2 y + 3 = 0

and

3 x + 4 y + 5 = 0

is:

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 9

The eccentricity of the conic

4 {(2 y - x - 3)}^{2} - 9 {(2 x + y - 1)}^{2} = 80

is:

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 10

The point of intersection of the curves whose parametric equations are

x = t^{2} + 1, y = 2 t

and

x = 2 s, y = \frac{2}{s}

is given by -

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 11

An ellipse has eccentricity

\frac{1}{2}

and one focus at the point

P (\frac{1}{2}, 1) .

Its one directrix is the common tangent nearer to the point

P,

to the circle

x^{2} + y^{2} = 1

and the hyperbola

x^{2} - y^{2} = 1 .

The equation of the ellipse in the standard form is