Question

Let A (2, 3), B (3, -6), C (5, - 7) be three points. If P is a point satisfying the condition PA² + PB² = 2 PC², then a point that lies on the locus of P is ______.

विकल्प

• (2, -5)

• (-2, 5)

• (13, 10)

• (-13, -10)

Answer 1

Let A (2, 3), B (3, -6), C (5, - 7) be three points. If P is a point satisfying the condition PA² + PB² = 2 PC², then a point that lies on the locus of P is (-13, -10).

Explanation:

Let P(x, y) be the point

PA² + PB² = 2 PC²

⇒ (x - 2)² + (y- 3)² + (x - 3)² + (y + 6)² = 2[(x - s)² + (y + 7)2]

⇒ 2x² + 2y² - 10x + 6y + 58 = 2x² + 2y² - 20x + 28y + 148

⇒ 10x - 22y = 90

⇒ 5x - 11y = 45

The above equation is locus of P.

Point (-13, -10) satisfies the above equation.