Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 20

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For parabola $y^{2} = 4 a x$ consider three points $A, B, C$ lying on it. If the centroid of $∆ A B C$ is $(h_{1}, k_{1}) &$ centroid of triangle formed by the point of intersection of tangents at $A, B, C$ has coordinates $(h_{2}, k_{2}),$ then which of the following is always true -

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Important Questions on Parabola

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 21

Equation

x^{2} - 2 x - 2 y + 5 = 0

represents -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 22

The normals to the parabola

y^{2} = 4 a x

from the point

(5 a, 2 a)

are -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 23

The equation of the lines joining the vertex of the parabola

y^{2} = 6 x

to the points on it whose abscissa is

24,

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 24

The equation of the tangent to the parabola

y^{2} = 9 x

which passes through the point

(4, 10)

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 25

Consider the equation of a parabola

y^{2} = 4 a x, (a < 0)

which of the following is false -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 26

The adjoining figure shows the graph of $y = a x^{2} + b x + c$ . Then

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-3>Q 10

If

' m'

varies and range of

c

for which the line

y = m x + c

touches the parabola

y^{2} = 8 (x + 2)

is

R - (- λ, λ),

then value of

λ

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-3>Q 11

Two tangents to the parabola

y^{2} = 8 x

meet the tangent at its vertex in the points

P & Q .

If

P Q = 4

units and the locus of the point of the intersection of the two tangents is

y^{2} = λ (x + 2),

then value of

\frac{10}{λ}

is