JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let

w=z\bar{z}+k_1z+k_2iz+\lambda(1+i)

k_1,k_2\in\mathbb{R}

. Let

\mathrm{Re}(w)=0

be the circle C of radius 1 in the first quadrant touching the line

y=1

and the

y

-axis. If the curve

\mathrm{Im}(w)=0

intersects C at A and B, then

30(AB)^2

is equal to ________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Power of a Point
Idea tested: Radical axis of two circles

Same idea in other shifts

Asked 3× in all

5 Apr 2024, Shift 2 · Q15Let the circle $C_1 : x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1, 0)$ and radius 2. If the line of the common chord…EasySingle correct
4 Sep 2020, Shift 2 · Q65The circle passing through the intersection of the circles, $x^2+y^2-6x=0$ and $x^2+y^2-4y=0$ , having its centre on the line,…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.