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

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If the normals drawn at the points $t_{1}$ and $t_{2}$ on the parabola meet the parabola again at its point $t_{3}$ , then $t_{1} t_{2}$ equals

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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 17

The length of the normal chord to the parabola

y^{2} = 4 x,

which subtends right angle at the vertex is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 18

The locus of the point of intersection of the normals at the ends of a focal chord of the parabola

y^{2} = 4 a x

is

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

The number of distinct normals that be drawn from

(- 2, 1)

to the parabola

y^{2} - 4 x - 2 y - 3 = 0

is

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

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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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} =