Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 13

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A rectangular hyperbola of latus rectum $4$ units passes through $(0, 0)$ and has $(2, 0)$ as its one focus. The equation of locus of the other focus is

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Important Questions on Hyperbola

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 14

If the curves

x^{2} - y^{2} = 4

and

x y = \sqrt{5}

intersect at points

A

and

B

, then the possible number of points

C

on the curve

x^{2} - y^{2} = 4

, such that triangle

A B C

is equilateral, is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 15

The point

(3 \tan (θ + 60 °), 2 \tan (θ + 30 °))

, where

θ

is the parameter, lies on the conic. Then its center is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 16

If

P (α, β),

the point of intersection of the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2} (1 - e^{2})} = 1

and the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{a^{2} (E^{2} - 1)} = \frac{1}{4}

is equidistant from the foci of the two curves (all lying on the right of

y

-axis), then

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 17

A hyperbola having transverse axis of length

\frac{1}{2}

unit is confocal with the ellipse

3 x^{2} + 4 y^{2} = 12

. Then

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 18

In the $x y$ plane, the path defined by the equation $\frac{1}{x^{m}} + \frac{1}{y^{m}} + \frac{k}{{(x + y)}^{n}} = 0$ is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 19

A point moves such that the sum of the squares of its distances from the two sides of length

a

of a rectangle is twice the sum of the squares of its distances from the other two sides of length

b

. The locus of the point can be

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 20

The equation of a hyperbola with co-ordinate axes as principal axes, and the distances of one of its vertices from the foci are

3

and

1

, can be

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 7 - Hyperbola>DPP>Q 1

The equation of a tangent to the hyperbola

3 x^{2} - y^{2} = 3

, parallel to the line

y = 2 x + 4

, is