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

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If the line $y - \sqrt{3} x + 3 = 0$ cuts the parabola $y^{2} = x + 2$ at $A$ and $B$ . If $P \equiv (\sqrt{3}, 0)$ then $P A \cdot P B$ 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 26

A ray of light moving parallel to

x

-axis gets reflected from a parabolic mirror whose equation is

4 (x + y) - y^{2} = 0 .

After reflection the ray pass through the point

(a, b)

. Then the value of

a + b

is

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

If the parabola

y = (a - b) x^{2} + (b - c) x + (c - a)

touches the

x

-axis then the line

a x + b y + c = 0

always passes through a fixed point is

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

The vertex of a parabola

y^{2} = 8 x

is at the centre of a circle and parabola cuts the circle at ends of its latus rectum. Then, equation of the circle is

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

The mirror image of the focus to the parabola

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

w.r.t. the directrix is

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

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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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