JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q11

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

Let

P(a, b)

be a point on the parabola

y^2 = 8x

such that the tangent at

P

passes through the centre of the circle

x^2 + y^2 - 10x - 14y + 65 = 0

. Let

A

be the product of all possible values of

a

and

B

be the product of all possible values of

b

. Then the value of

A + B

is equal to

(1)0
(2)25
(3)40
(4)65Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Tangent to General Conic (T=0)

Same idea in other shifts

Asked 6× in all

25 Jul 2022, Shift 2 · Q13The tangents at the points $A(1,3)$ and $B(1,-1)$ on the parabola $y^2-2x-2y=1$ meet at the point $P$ . Then the area (in unit $^2$ ) of the…MediumSingle correct
30 Jul 2022, Shift 2 · Q86Let $A\,(0, a+2)$ , $B\,(0, a)$ , $C\,(-2, 0)$ and $D\,(2, 0)$ be four points and the lines $AD$ and $BC$ intersect at $P\,(x, y)$ . If the…MediumNumerical value
26 Aug 2021, Shift 2 · Q72The point $\mathrm{P}(-2\sqrt{6},\sqrt{3})$ lies on the hyperbola $\frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{b}^2}=1$ having…HardSingle correct
24 Feb 2021, Shift 2 · Q64For which of the following curves, the line $x+\sqrt{3}y=2\sqrt{3}$ is the tangent at the point…EasySingle correct
8 Jan 2020, Shift 2 · Q74Let a line $y = mx$ $(\mathrm{m} > 0)$ intersect the parabola, $y^2 = x$ at a point P, other than the origin. Let the tangent to it at P…MediumNumerical value

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.