A variable circle passes through the fixed point A(p,q) and touches x-axis. he locus of  the other end of the diameter through ‘A’ is

Let B(x1,y1)  be the other end of diameter.∴ The equation of the circle with AB  as diameter is (x−p)(x−x1)+(y−y1)(y−q)=0⇒x2+y2−x(p+x1)−y(q+y1)+px1+qy1=0⇒ 2g=-(p+x1)            c=px1+qy1Since circle touches x-axis⇒g2=c⇒(p+x1)24=px1+qy1⇒(x1−p)2=4qy1∴ locus is (x−p)2=4qy