Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20257 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Parabola

JEE Main 2025 · 7 April · Morning Shift · Mathematics · Parabola

Let P be the parabola, whose focus is (-2,1) and directrix is 2...

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 , is 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

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

Options

A $\frac{3}{2}$
B $\frac{5}{2}$
C $\frac{1}{4}$
D $\frac{3}{4}$

Correct answer

A. $\frac{3}{2}$

Step-by-step solution

Equation of parabola

(x+2)^2+(y-1)^2=\left(\frac{2 x+y+2}{\sqrt{5}}\right)^2<br/><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/qZ3Y8sfiWupYB2A7M7C8hxcWRQvBpUEFE3t7VgevHOM.original.fullsize.png"/><br/>

5\left[(x+2)^2+(y-1)^2\right]=(2 x+y+2)^2

<br/>Put

x=-2,5(y-1)^2=(y-2)^2

<br/>

\begin{aligned}<br/>& 5\left(y^2-2 y+1\right)=y^2-4 y+4 \\ & \Rightarrow 4 y^2-6 y+1=0 \Rightarrow y_1+y_2=\frac{3}{2}<br/>\end{aligned}

$

Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the… JEE Advanced 2026 Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026 Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026 Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026 Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026 Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026 Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026 Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026 Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026 Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026 An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026 Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026 If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026 Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026 Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026 Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs