Question

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 ______.

Options

• 13

• 14

• 15

• 16

Answer 1

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 16.

Explanation:

Let point be P(x, y), then x² + y² + (x – 0)² + (y – 1)² + (x – 1)² + (y – 0)² + (x – 1)² + (y – 1)² = 18

⇒ 4x² + 4y² – 4x – 4y + 4 = 18

⇒ `x^2 + y^2 - x - y - 14/4` = 0

∴ Centre = `(1/2, 1/2)`

r = `sqrt(1/4 + 1/4 + 14/4)` = 2

∴ d = 2r = 2(2) = 4

So, d² = 16