Question

Find the locus of a point P if the join of the points (2,3) and (-1,5) subtends a right angle at P​

Answer 1

Answer:

Let P = (x, y) and A(2, 3), B(–1, 5) be the given points. Given condition is =>APB = 90° => PA2 + PB2 = AB2 => (x – 2)2 + (y – 3)2 + (x + 1)2 + (y – 5)2 = (–1 – 2)2 + (5 – 3)2 => x2 – 4x + 4 + y2 – 6y + 9 + x2 + 2x + 1 + y2 – 10y + 25 = 9 + 4 => 2x2 + 2y2 – 2x – 16y + 26 = 0 => x2 + y2 – x – 8y + 13 = 0 => The locus of P is x2 + y2 – x – 8y + 13 = 0.Read more on Sarthaks.com - https://www.sarthaks.com/440852/find-the-locus-of-a-point-p-if-the-line-joining-the-points-2-3-and-1-5-subtends-a-right-angle-at-p?show=440863#a440863