JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q10

MathematicsSingle correct+4 / -1Question 10 of 90

A circle touches both the $y$ -axis and the line $x+y=0$ . Then the locus of its center is:

y=\sqrt2x

x=\sqrt2y

y^2-x^2=2xy

x^2-y^2=2xy

Answer and worked solution

Official answer: D

Centre $(h,k)$ . Touching the $y$ -axis: $r=|h|$ . Touching $x+y=0$ : $r=\dfrac{|h+k|}{\sqrt2}$ .

Locus. $2h^2=(h+k)^2$ gives $h^2-2hk-k^2=0$ , i.e. $x^2-y^2=2xy$ .

(D)

JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 10