JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Circle

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

d^{2}

is equal to ____.

Answer: 16

Solution

Let the moving point be

(x, y)

. The sum of squares of distances is:

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

Expanding:

4 x^{2} + 4 y^{2} - 4 x - 4 y + 4 = 18

, which simplifies to

x^{2} + y^{2} - x - y = \frac{7}{2}

.

Completing the square:

(x - \frac{1}{2})^{2} + (y - \frac{1}{2})^{2} = 4

. This is a circle with radius

r = 2

, so diameter

d = 4

and

d^{2} = 16

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Integer answer

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