Question

If A and B are two fixed points, then the locus of a point which moves in such a way that the ∠APB is a right angle, is

(a) a circle 

(b) an ellipse

(c) a parabola 

(d) None of these

Answer 1

Correct option: (a) a circle

Explanation: 

Let A (x₁, y₁) and B( x₂, y₂) be two fixed points.

Let P(h,k) be a variable point such that ∠APB is a right angle.

Since AP and BP are two lines that intersects at right angle

Then, slope of AP x slope of BP = -1

which is a circle with AB as diameter.