Question

A tangent is drawn to each of the circles x2 + y2 = a2, x2 + y2 = b2. Show that if these two tangents are perpendicular to each other, the locus of their point of intersection is a circle concentric with the given circles.

Answer 1

The locus of the point of intersection of two perpendicular tangents drawn to two circles is a circle concentric with the given circles.

Step-by-step explanation:

To show that the locus of the point of intersection of two tangents drawn to the circles x2 + y2 = a2 and x2 + y2 = b2 is a circle concentric with the given circles, we can use the property of perpendicular tangents to circles. Let the point of intersection be P(x, y). Since P is on both tangents, the distances from P to the centers of the circles will be equal to the radii of the circles. Therefore, the locus of P will be a circle with the same center as the given circles.