Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 70

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If $e_{1}$ be the eccentricity of the conic $9 x^{2} + 4 y^{2} = 36$ and $e_{2}$ is the eccentricity of the conic $9 x^{2} - 4 y^{2} = 36$ and $e_{3}$ be the eccentricity of conic $x^{2} - y^{2} = 36$ then $18 (e_{1}^{2} + e_{2}^{2}) \cdot e_{3}^{2}$ is equal to -

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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 1

Three normals are drawn to curve

y^{2} = x

from a point

(c, 0) .

Out of three one is always in x-axis. If two other normal are perpendicular to each other, then the values of

c

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 2

If the line

\frac{x}{a} + \frac{y}{b} = \sqrt{2}

touches the ellipse

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

at

P

, then eccentric angle of the points is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 3

The tangent at any point on the ellipse

16 x^{2} + 25 y^{2} = 400

meets the tangents at the ends of the major axis at

T_{1}

and

T_{2}

. The circle on

T_{1} T_{2}

as diameter passes through

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 4

If

C D

is a diameter of an ellipse

x^{2} + 9 y^{2} = 25

and the eccentric angle of

C

is

\frac{π}{6}

, then the eccentric angle of

D

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 5

If

θ_{1}, θ_{2}, θ_{3}, θ_{4}

be eccentric angles of the four concyclic points of the ellipse

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

, then

θ_{1} + θ_{2} + θ_{3} + θ_{4}

is

(

where

n \in I)

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 8

Area of the region bounded by the curve

\{(x, y) : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1 \leq \frac{x}{a} + \frac{y}{b}\}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 9

The ellipse

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

is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point

(4, 0)

. Then the equation of the ellipse is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 10

If

P Q

is a double ordinate of the 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