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JEE Advanced

IMPORTANT

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$P Q$ and $R S$ are two perpendicular chords of the rectangular hyperbola $x y = c^{2}$ . If $C$ is the centre of the rectangular hyperbola, then the product of the slopes of $C P, C Q, C R$ and $C S$ is equal to

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Important Questions on Hyperbola

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 49

If a circle cuts the rectangular hyperbola

x y = 1

in the points

(x_{r}, y_{r}); r = 1, 2, 3, 4

then

x_{1} x_{2} x_{3} x_{4} = y_{1} y_{2} y_{3} y_{4}

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 50

The product of the perpendicular from any point on the hyperbola

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

to its asymptotes, is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 51

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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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 52

If four points are taken on a rectangular hyperbola such that the chord joining any two is perpendicular to the chord joining the other two and

α, β, γ, δ

are the inclinations to either asymptote of the straight line joining these points to the centre, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 53

Let

P

be a point on the hyperbola

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

, where

a

is a parameter such that

P

is nearest to the line

y = 2 x

. Then, the locus of

P

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 54

The coordinates of the point of intersection of two tangents to a rectangular hyperbola referred to its asymptote as axes, are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 55

From any point

P (h, k)

, four normals can be drawn to the rectangular hyperbola

x y = c^{2}

such that sum of the ordinates of the feet of the normals is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Target Exercises>Q 56

From any point

P (h, k)

, four normals can be drawn to the rectangular hyperbola

x y = c^{2}

such that product of the abscissae of the feet of the normals

=

product of the ordinates of the feet of the normals is equal to

PQ and RS are two perpendicular chords of the rectangular hyperbola xy=c2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CP, CQ, CR and CS is equal to

Important Questions on Hyperbola

Learn and Prepare for any exam you want !

$P Q$ and $R S$ are two perpendicular chords of the rectangular hyperbola $x y = c^{2}$ . If $C$ is the centre of the rectangular hyperbola, then the product of the slopes of $C P, C Q, C R$ and $C S$ is equal to