Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 2>Q 8

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IMPORTANT

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The locus of a perpendicular from the center upon the normal to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is

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Important Questions on Hyperbola

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 2>Q 9

The locus of the foot of the perpendicular from the centre of the hyperbola

x y = 1

on a variable tangent is

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Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 3>Q 1

If two points

P

and

Q

on the hyperbola

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

whose centre

C

be such that

C P

is perpendicular to

C Q, a < b,

then the value of

\frac{1}{C P^{2}} + \frac{1}{C Q^{2}}

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 3>Q 2

If a chord joining

P (a \sec θ, a \tan θ)

and

Q (a \sec α, a \tan α)

on the hyperbola

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

is the normal at

P

, then

\tan α

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 3>Q 3

If

P Q

is a double ordinate of 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

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 3>Q 4

The foci of a hyperbola coincide with the foci of the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1

. If the eccentricity of the hyperbola is

2

, then the equation of the tangent to this hyperbola passing through the point

(4, 6)

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 13 - Hyperbola>Level 3>Q 5

A square

A B C D

has all its vertices on the curve

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

The midpoints of its sides also lie on the same curve. Then, the square of area of

A B C D

is