New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Parabola question

2025 · 2 Apr · Shift 1 · Q31

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Parabola
2025 · 2 Apr · Shift 1 · Q31

Parabola question

2025 · 2 Apr · Shift 1 · Q31

JEE MainMathematicsParabolaMCQ+4 / −1

Let the focal chord PQ of the parabola

y^2=4 x

make an angle of

60^{\circ}

with the positive

x

axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the

y

-axis at the point

(0, \alpha)

, then

5 \alpha^2

is equal to:

A
15
B
25
C
20
D
30

More from Parabola

Let the point P of the focal chord PQ of the parabola $y^{2} = 16 x$ be $(1, - 4)$ . If the focus of the parabola divides the chord $P Q$ in the ratio $m : n, gcd (m, n) = 1$ , then $m^{2} + n^{2}$ is equal to :2025 · MCQ
The radius of the smallest circle which touches the parabolas $y = x^{2} + 2$ and $x = y^{2} + 2$ is2025 · MCQ
A line passing through the point $A (- 2, 0)$ , touches the parabola $P : y^{2} = x - 2$ at the point $P$ in the first quadrant. The area, of the region bounded by the line $x$ , parabola $P$ and the $x$ -axis, is :2025 · MCQ
The axis of a parabola is the line $y = x$ and its vertex and focus are in the first quadrant at distances $2$ and $22$ units from the origin, respectively. If the point $(1, k)$ lies on the parabola, then a possible value of…2025 · MCQ
Let P be the parabola, whose focus is $(- 2, 1)$ and directrix is $2 x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose abscissa is $-$ 2, is2025 · MCQ
Let $r$ be the radius of the circle, which touches $x$ - axis at point $(a, 0), a < 0$ and the parabola $y^{2} = 9 x$ at the point $r$ . Then $r$ is equal to .2025 · Numerical
Let the parabola $y = x^{2} + p x - 3$ , meet the coordinate axes at the points $P, Q$ and R . If the circle C with centre at $(- 1, - 1)$ passes through the points $P, Q$ and $R$ , then the area of $△ P QR$ is :2025 · MCQ
Let $P (4, 43)$ be a point on the parabola $y^{2} = 4 a x$ and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the…2025 · MCQ