Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 16

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Chord of contact of tangents drawn from the point $M (h, k)$ to the ellipse $x^{2} + 4 y^{2} = 4$ intersects at $P$ and $Q$ , subtends a right angle of the centre $' O'$

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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 18

If a quadrilateral formed by four tangents to the ellipse

3 x^{2} + 4 y^{2} = 12

is a square, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 19

Let

(α, β)

be a point from which two perpendicular tangent can be drawn to the ellipse

4 x^{2} + 5 y^{2} = 20

. If

F = 4 α + 3 β

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 20

Equation of a tangent passing through

(2, 8)

to the hyperbola

5 x^{2} - y^{2} = 5

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 21

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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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 22

Let

A B

be a double ordinate of hyperbola

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

. If

O

be the centre of the hyperbola and

O A B

is an equilateral triangle, then which of the following is/are true, if

A (α, β)

?

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 23

The angle between a pair of tangents drawn from a point

P

to the parabola

y^{2} = 4 a x

is

45 °

, if locus of point

P

is hyperbola then its foci are

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 24

Which of the following is/are true for locus represented by $x = \frac{1}{2} a (t + \frac{1}{t}), y = \frac{1}{2} a (t - \frac{1}{t})$ ? ( Here, $t$ is parameter)

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 25

If line joining point

(0, 3)

and

(5, - 2)

is tangent to curve

y = \frac{1}{x + c}

, then value of

c

is/are