Given two fixed points A ( - 2 , 1 ) and B ( 3 , 0 ) , find the locus of a point P which moves such that the angle ∠ A P B is always a right angle.

Step-by-step solution

Let, the coordinates of point P h ,   k Given, points A - 2 ,   1 and B 3 ,   0 , So, the slope of A P is (Say m 1 ) k - 1 h + 2 , and, the slope of B P is (Say m 2 ) k - 0 h - 3 = k h - 3 As, ∠ A P B = 90 ° Hence, m 1 m 2 = - 1 k - 1 h + 2 × k h - 3 = - 1   ⇒   k 2 - k h 2 + 2 h - 3 h - 6 = - 1   ⇒ k 2 - k h 2 - h - 6 = - 1   k 2 - k = - h 2 - h - 6   ⇒   k 2 + h 2 - k - h - 6 = 0 So, replace h ,   k → x ,   y , in order