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

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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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Important Questions on Hyperbola

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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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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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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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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

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 12

If

H (x, y) = 0

represents the equation of a hyperbola and

A (x, y) = 0, C (x, y) = 0

are the equation of its asymptotes and the conjugate hyperbola respectively, then for any point

(α, β)

in the plane;

H (α, β), A (α, β)

and

C (α, β)

are in

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 13

If a triangle is inscribed in a rectangular hyperbola, its orthocentre lies:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 14

If the tangent and normal to a rectangular hyperbola cut off intercepts

x_{1}

and

x_{2}

on one axis and

y_{1}

and

y_{2}

on the other axis, then:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 7 - Hyperbola>Multiple Choice I>Q 15

If

P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3})

and

S (x_{4}, y_{4})

are four concyclic points on the rectangular hyperbola

x y = c^{2}

, then coordinates of orthocentre of

Δ P Q R

are