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

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Let $m_{1}, m_{2}$ are slopes of two tangents that are drawn from $(2, 3)$ to the parabola $y^{2} = 4 x$ and $α$ is the harmonic mean of $m_{1} & m_{2}$ . If $β$ is the value of $(1 + \tan 23 °) (1 + \tan 22 °)$ , then $\frac{3}{2} α + β$ is

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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 31

The point on the curve

y^{2} = 4 x

which is nearest to the point

(2, 1)

is

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

The eccentricity of the ellipse, which passes through the points

(2, - 2)

and

(- 3, 1)

is

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

In an ellipse the distance between the foci is

8

and the distance between the directrices is

25

, then the ratio of the length of major and minor axis is

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

If the focal distance of an end of the minor axis of an ellipse, whose axes along the

x

and

y

axes respectively is

k

and the distance between the foci is

2 h

. Then the equation of the ellipse is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 38

The number of values of

c

, such that

y = 4 x + c

touches

\frac{x^{2}}{4} + y^{2} = 1

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 39

The sum of the squares of the perpendiculars on any tangent to the ellipse

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

from two points on the minor axis each at a distance

\sqrt{a^{2} - b^{2}}

from the centre is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 40

The line

2 x + y = 3

cuts the ellipse

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

at

P

and

Q

. If $\theta$ be the angle between the normals at these points, then

\tan θ

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 41

Number of points on the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

from which pair of perpendicular tangents are drawn to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, is