A circle cuts a chord of length 4 a on the x -axis and passes through a point on the y -axis, distant 2 ~b from the origin. Then the locus of the centre of this circle, is:

Step-by-step solution

Let centre be C(h, k)C Q=C P=r C Q²=C P²(h-0)²+(k 0)²=C M²+M P²h²+(k 2 ~b )²=k²+4 a²h²+k²+4 b² 4 b k=k²+4 a² Then, the locus of centre C(h, k)x²+4 b² 4 b y=4 a² Hence, the above locus of the centre of circle is a parabola.