List of top Mathematics Questions on Parabola asked in JEE Main

If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points A and B, then at the vertex of the parabola, the line segment AB subtends an angle equal to:

Let $P(4, 4\sqrt{3})$ be a point on the parabola $y^2 = 4ax$ and PQ be a focal chord of the parabola. If M and N are the foot of the perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to:

Let A and B be the two points of intersection of the line $y + 5 = 0$ and the mirror image of the parabola $y^2 = 4x$ with respect to the line $x + y + 4 = 0$ . If $d$ denotes the distance between A and B, and $a$ denotes the area of $\Delta SAB$ , where $S$ is the focus of the parabola $y^2 = 4x$ , then the value of $(a + d)$ is:

Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at points A and B, then $(AB)^2$ is equal to:

Let $y^2 = 12x$ be the parabola and $S$ its focus. Let $PQ$ be a focal chord of the parabola such that $(SP)(SQ) = \frac{147}{4}$ . Let $C$ be the circle described by taking $PQ$ as a diameter. If the equation of the circle $C$ is: $64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta,$ then $\beta - \alpha$ is equal to:

The area of the region enclosed by the parabolas

y = 4 – x^2

and

3y = (x – 4)^2

is in (sq. unit)?

(α, β)

lie on the parabola

y^2 = 4x

and

(α, β)

also lie on chord with midpoint

(1,\frac 54)

of another parabola

x^2 = 8y

, then value of

|(8 – β)(α – 28)|

is

Let the length of the focal chord

PQ

of the parabola

y^2 = 12x

be 15 units. If the distance of

PQ

from the origin is

p

, then

10p^2

is equal to _____

The area (in square units) of the region described by:

\{(x, y) : y^2 \leq 2x, \, \text{and} \, y \geq 4x - 1\}

is:

Let

L_1, L_2

be the lines passing through the point

P(0, 1)

and touching the parabola

9x^2 + 12x + 18y - 14 = 0.

Let

Q

and

R

be the points on the lines

L_1

and

L_2

such that the

\Delta PQR

is an isosceles triangle with base

QR

. If the slopes of the lines

QR

are

m_1

and

m_2

, then

16\left(m_1^2 + m_2^2\right)

is equal to ______.

Let

C

be the circle of minimum area touching the parabola

y = 6 - x^2

and the lines

y = \sqrt{3} |x|

. Then, which one of the following points lies on the circle

C

?

Let

PQ

be a chord of the parabola

y^2 = 12x

and the midpoint of

PQ

be at

(4, 1)

. Then, which of the following points lies on the line passing through the points

P

and

Q

?

The area of the region enclosed by the parabola

(y - 2)^2 = x - 1

, the line

x - 2y + 4 = 0

and the positive coordinate axes is ______.

If the shortest distance of the parabola $y^{2}=4x$ from the centre of the circle $x² + y² - 4x - 16y + 64 = 0$ is d, then d²is equal to:

Let R be the focus of the parabola y² = 20x and the line y=mx+c intersect the parabola at two points Pand Q. Let the point G(10,10) be the centroid of the triangle PQR. If c-m=6, then (PQ)² is

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

If

P ( h , k )

be a point on the parabola

x=4 y^2

, which is nearest to the point

Q (0,33)

, then the distance of

P

from the directrix of the parabola

y^2=4(x+y)

is equal to :

Let PQ be a focal chord of the parabola y² = 36x of length 100, making an acute angle with the positive x-axis. Let the ordinate of P be positive and M be the point on the line segment PQ such that PM:MQ = 3:1. Then which of the following points does

\underline{NOT}

lie on the line passing through M and perpendicular to the line PQ?

Let $S$ be the set of all $a \in N$ such that the area of the triangle formed by the tangent at the point $P ( b, c), b, c \in N$ , on the parabola $y^2=2$ ax and the lines $x=b, y=0$ is $16$ unit ${ }^2$ , then $\displaystyle\sum_{a \in S} a$ is equal to _____