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

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The normal at any point $P (t^{2}, 2 t)$ on the parabola $y^{2} = 4 x$ meets the curve again at $Q$ , then the $ar (Δ P O Q)$ in $m$ the form of $\frac{k}{| t |} (1 + t^{2}) (2 + t^{2})$ . Find the value of $k$ :

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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 21

If the segment intercepted by the parabola

y^{2} = 4 a x

with the line

ℓ x + m y + n = 0

subtends a right angle at the vertex, then

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

The line

y = a - x

touches the parabola

y = x - x^{2}

and

f (x) = \sin^{2} x + \sin^{2} (x + \frac{π}{3}) + \cos x \cdot \cos (x + \frac{π}{3})

then

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

The coordinates of the point on the parabola

y^{2} = 8 x

which is at a minimum distance from the circle

x^{2} + {(y + 6)}^{2} = 1

are

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

If a circle intersects the parabola

y^{2} = 4 a x,

at points

A (a t_{1}^{2}, 2 a t_{1}), B (a t_{2}^{2}, 2 a t_{2}), C (a t_{3}^{2}, 2 a t_{3}), D (a t_{4}^{2}, 2 a t_{4})

then

t_{1} + t_{2} + t_{3} + t_{4} =

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

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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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