Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 27

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The locus of a point whose chord of contact w.r.t the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ touches the circle in-scribed on the straight line joining the foci of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ as diameter is/has

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Important Questions on Conic Section

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 28

The normal to the hyperbola

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

meets the axes in

M

and

N

, and lines

M P

and

N P

are drawn at right angle to the axes then locus of

P

is a hyperbola with eccentricity

e'

, if eccentricity of

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

is

e

then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 29

If the axis of a varying central hyperbola

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

be fixed in magnitude and position, then locus of point of contact of a tangent drawn to it from a fixed point on

x

-axis is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 30

If

e_{1}

and

e_{2}

are the eccentricity of hyperbola

x y = c^{2}

and

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

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 31

If equation of hyperbola is

x y + 3 x - 2 y - 10 = 0

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 32

If

(5, 12)

and

(24, 7)

are the foci of a conic passing through origin, then eccentricity of the conic is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 33

If equation of hyperbola is

2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 35

If the normals at

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

on the rectangular hyperbola

x y = c^{2}

meet at the point

(α, β)

,then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 36

The locus of feet of the normals to

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

from

(h, k)

is