Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 9

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If the normals from any point to the parabola $x^{2} = 4 y$ cuts the line $y = 2$ in points whose abscissae are in $A P$ , then the slopes of the tangents at the three conormal points are in :

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Important Questions on Parabola

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 10

Let the line

l x + m y = 1

cut the parabola

y^{2} = 4 a x

in the points

A

and

B

. Normals at

A

and

B

meet at point

C

. Normal from

C

other than these two meet the parabola at

D

then the co-ordinates of

D

are :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 11

The triangle formed by the tangent to the parabola

y = x^{2}

at the point whose abscissa is

x_{0}; x_{0} \in [1, 2]

, the

y

-axis and the straight line

y = x_{0}^{2}

has the greatest area if

x_{0}

equal to:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 12

A line

L

passing through the focus of the parabola

y^{2} = 4 (x - 1)

intersects the parabola in two distinct points. If

' m'

be the slope of the line

L

then

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 13

If the tangents to the parabola

y^{2} = 4 a x

at the points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

meet at the point

(x_{3}, y_{3})

then :

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 15

The latus rectum of the parabola

x = a t^{2} + b t + c, y = a' t^{2} + b' t + c'

is:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice II>Q 1

Let

P Q

be a chord of the parabola

y^{2} = 4 x .

A circle drawn with

P Q

as a diameter passes through the vertex

V

of the parabola. If area of

(∆ P V Q) = 20 {unit}^{2}

, then the coordinates of

P

are

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice II>Q 2

Consider a circle with its centre lying on the focus of the parabola

y^{2} = 2 p x

such that it touches the directrix of the parabola. Then the point of intersection of the circle and the parabola is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice II>Q 3

A tangent to the parabola

y^{2} = 4 a x

is inclined at

\frac{π}{3}

with the axis of the parabola. The point of contact is