Verified Solution • 2025–26 Session moderate

QJEEM21Ma68e2: JEE Main 2021 Mathematics - Class 11 JEEM21Ma68e2 Solution: The locus of a point, which moves such that the sum of squares…

The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter d. Then d2 is equal to _____________.

Step-by-Step Verified Solution

Let point P(x, y)

A(0, 0), B(1, 0), C(0, 1), D(1, 1)

(PA)2 + (PB)2 + (PC)2 + (PD)2 = 18

x2+y2+x2+(y−1)2+(x−1)2+y2+(x−1)2+(y−1)2{x^2} + {y^2} + {x^2} + {(y - 1)^2} + {(x - 1)^2} + {y^2} + {(x - 1)^2} + {(y - 1)^2} = 18

⇒4(x2+y2)−4y−4x=14\Rightarrow 4({x^2} + {y^2}) - 4y - 4x = 14

⇒x2+y2−x−y−72=0\Rightarrow {x^2} + {y^2} - x - y - {7 \over 2} = 0

d=214+14+72d = 2\sqrt {{1 \over 4} + {1 \over 4} + {7 \over 2}}

⇒d2=16\Rightarrow {d^2} = 16

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring