Question

A variable chord is drawn through the origin to the circle x²+y²−2ax=0. What is the locus of the center of the circle drawn on this chord as its diameter?

Answer 1

The locus of the center of the circle drawn on the chord as its diameter is a circle with center (0, 0) and radius a.

Step-by-step explanation:

The locus of the center of the circle drawn on the variable chord is another circle. The equation of the given circle is x² + y² - 2ax = 0. Since the chord passes through the origin, the coordinates of the two endpoints of the chord are (-a, 0) and (a, 0). The midpoint of the chord, which is also the center of the circle, is (0, 0). Therefore, the locus of the center of the circle drawn on the chord as its diameter is the circle with center (0, 0) and radius a.