JEE Main 2026 · 2 Apr · Shift 1 · Mathematics Q24

← JEE Main 2026 · 2 Apr · Shift 1

MathematicsInteger+4 / -1Question 24 of 75

Let a circle $C$ have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of $C$ on the line $x+y=1$ is $\sqrt{14}$ , then the square of the radius of $C$ is ________.

Your answer

Answer and worked solution

Official answer: 8

Three intersection points with equal intercepts means the circle passes through the origin: $x^2+y^2-2hx-2hy=0$ , centre $(h,h)$ , $r^2=2h^2$ .

Chord on $x+y=1$ . Distance from the centre is $\frac{|2h-1|}{\sqrt2}$ , so
$2h^2=\frac{(2h-1)^2}2+\frac{14}4\implies4h^2=4h^2-4h+8\implies h=2.$

Radius. $r^2=8$ .

Answer: 8

Topics:Equation of a circle Distance of a point from a line

← Previous question Next question →

JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 24