Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 41

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The equation of common tangent of $x^{2} + y^{2} - 8 x = 0$ and $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ with positive slope is

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Important Questions on Hyperbola

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 42

If the tangent and the normal to the hyperbola

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

at a point cut off intercepts

a_{1}

and

a_{2}

, respectively on the

X

-axis, and

b_{1}

and

b_{2}

, respectively on the

Y

-axis, then the value of

a_{1} a_{2} + b_{1} b_{2}

is

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 43

Let

P (a secθ, b tanθ)

and

Q (a \sec ϕ, b \tan ϕ)

where

θ + ϕ = \frac{π}{2},

be two points on the hyperbola

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

If

(h, k)

is the point of intersection of the normals at

P

and

Q,

then

k

is equal to-

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 44

Tangents are drawn from any point on the hyperbola

\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1

to the circle

x^{2} + y^{2} = 9,

then the locus of midpoint of the chord of contact is

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 45

If chords of the hyperbola

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

touch the parabola

y^{2} = 4 a x .

Then, the locus of their middle point is

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 46

If the circle

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

intersects the hyperbola

x y = c^{2}

in four points

P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), S (x_{4}, y_{4})

, then

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 47

If the line

a x + b y + c = 0

is a normal to the curve

x y = 1

, then

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 48

If the normal at

(c t, \frac{c}{t})

on the curve

x y = c^{2}

meets the curve again at

t^{'}

, then

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 49

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

x y = c^{2}

on a variable tangent is: