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

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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

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Important Questions on Parabola

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-3>Q 12

The radius of circle which passes through the focus of the parabola

x^{2} = 4 y &

touches it at the point

(6, 9)

is

a \sqrt{10},

then value of

' a'

is

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-3>Q 13

In the parabola

y^{2} = 4 a x,

the tangent at the point

P,

whose abscissa is equal to the latus rectum meets the axis in

T &

the normal at

P

cuts the parabola again at

Q .

If

P T : P Q = a : b

(where

a

and

b

are relative prime), then find value of

(\frac{b}{a})

.

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-3>Q 14

If the locus of a point, such that two of the three normals drawn from it to the parabola

y^{2} = 4 a x

are perpendicular is

y^{2} = a (x - λ a),

then value of

λ

is

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-3>Q 15

If the normal at

P (18, 12)

to the parabola

y^{2} = 8 x

cuts it again at

Q

, if

P Q = \frac{80 \sqrt{10}}{λ},

then value of

λ

is

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 1

If the end points

P (t_{1})

and

Q (t_{2})

of a chord of a parabola

y^{2} = 4 a x

satisfy the relation

t_{1} t_{2} = k

(constant) then prove that the chord always passes through a fixed point. Find that point also?

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 2

Find the locus of the middle points of all chords of the parabola

y^{2} = 4 a x

which are drawn through the vertex.

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 5

Two perpendicular chords are drawn from the origin

' O'

to the parabola

y = x^{2}

, which meet the parabola at

P

and

Q

Rectangle

P O Q R

is completed. Find the locus of vertex

R

.

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 6

Find the set of values of

α

in the interval

[\frac{π}{2}, \frac{3 π}{2}]

for which the point

(\sin α, \cos α)

does not lie outside the parabola

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