MEDIUM

JEE Main

IMPORTANT

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Let $P : y^{2} = 4 a x, a > 0$ be a parabola with focus $S$ .Let the tangents to the parabola $P$ make an angle of $\frac{π}{4}$ with the line $y = 3 x + 5$ touch the parabola $P$ at $A$ and $B$ . Then the value of $a$ for which $A, B$ and $S$ are collinear is:

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Important Questions on Parabola

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 July 2022 Shift 1>Q 63

The sum of diameters of the circles that touch the parabola

75 x^{2} = 64 (5 y - 3)

at the point

(\frac{8}{5}, \frac{6}{5})

and the

y

-axis, is equal to _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 July 2022 Shift 2>Q 64

The tangents at the points

A (1, 3)

and

B (1, - 1)

on the parabola

y^{2} - 2 x - 2 y = 1

meet at the point

P

. Then the area (in

{unit}^{2}

) of the triangle

P A B

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 26 July 2022 Shift 1>Q 65

Let the function

f (x) = 2 x^{2} - \log_{e} x, x > 0

, be decreasing in

(0, a)

and increasing in

(a, 4)

. A tangent to the parabola

y^{2} = 4 a x

at a point

P

on it passes through the point

(8 a, 8 a - 1)

but does not pass through the point

(- \frac{1}{a}, 0)

. If the equation of the normal at

P

\frac{x}{α} + \frac{y}{β} = 1

, then

α + β

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 26 July 2022 Shift 2>Q 66

Let

P

and

Q

be any points on the curves

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

and

y = x^{2}

, respectively. The distance between

P

and

Q

is minimum for some value of the abscissa of

P

in the interval

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 26 July 2022 Shift 2>Q 67

The equation of a common tangent to the parabolas

y = x^{2}

and

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 27 July 2022 Shift 1>Q 68

Let

P (a, b)

be a point on the parabola

y^{2} = 8 x

such that the tangent at

P

passes through the centre of the circle

x^{2} + y^{2} - 10 x - 14 y + 65 = 0

. Let

A

be the product of all possible values of

a

and

B

be the product of all possible values of

b

. Then the value of

A + B

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 27 July 2022 Shift 2>Q 69

If the length of the latus rectum of a parabola, whose focus is

(a, a)

and the tangent at its vertex is

x + y = a

, is

16

, then

|a|

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 28 July 2022 Shift 1>Q 70

If the tangents drawn at the points

P

and

Q

on the parabola

y^{2} = 2 x - 3

intersect at the point

R (0, 1)

, then the orthocentre of the triangle

P Q R

Let P:y2=4ax, a>0 be a parabola with focus S.Let the tangents to the parabola P make an angle of π4 with the line y=3x+5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is:

Important Questions on Parabola

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Let $P : y^{2} = 4 a x, a > 0$ be a parabola with focus $S$ .Let the tangents to the parabola $P$ make an angle of $\frac{π}{4}$ with the line $y = 3 x + 5$ touch the parabola $P$ at $A$ and $B$ . Then the value of $a$ for which $A, B$ and $S$ are collinear is: