Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20254 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 4 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Parabola

JEE Main 2025 · 4 April · Evening Shift · Mathematics · Parabola

The axis of a parabola is the line y=x and its vertex and focus are...

The axis of a parabola is the line

y=x

and its vertex and focus are in the first quadrant at distances

\sqrt{2}

and

2 \sqrt{2}

units from the origin, respectively. If the point

(1, \mathrm{k})

lies on the parabola, then a possible value of

k

is :-

Options

A $4$
B $9$
C $3$
D $8$

Correct answer

B. $9$

Step-by-step solution

Directrix

x+y=0

\begin{aligned}& \mathrm{PS}=\mathrm{PM} \\ & \sqrt{(1-2)^2+(\mathrm{K}-2)^2}=\frac{(1+\mathrm{K})}{\sqrt{2}} \\ & 2 \mathrm{ K}^2+8-8 \mathrm{ K}+2=\mathrm{K}^2+1+2 \mathrm{ K} \\ & \mathrm{ K}^2-10 \mathrm{ K}+9=0 \\ & \mathrm{ K}=9 \\ & \text{ option (2) }\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