JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

If the equation of the parabola, whose vertex is at

(5, 4)

and the directrix is

3x+y-29=0

, is

x^2+ay^2+bxy+cx+dy+k=0

, then

a+b+c+d+k

is equal to

(1) $575$
(2) $-575$
(3) $576$
(4) $-576$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Focus-Directrix Form Extraction

Same idea in other shifts

Asked 4× in all

7 Apr 2025, Shift 1 · Q10Let P be the parabola, whose focus is $(-2, 1)$ and directrix is $2x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose…MediumSingle correct
25 Jun 2022, Shift 1 · Q19Let $x=2t$ , $y=\frac{t^2}{3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $SA\perp BA$ , where A…HardSingle correct
24 Feb 2021, Shift 1 · Q74The locus of the mid-point of the line segment joining the focus of the parabola $y^2 = 4ax$ to a moving point of the parabola, is another…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.