Let the other end of diameter is (h,k) then equation of circle is (x−h)(x−p)+(y−k)(y−q)=0 Put y=0, since x-axis touches the circle ⇒x2−(h+p)x+(hp+kq)=0⇒(h+p)2=4(hp+kq)(D=0)⇒(x−p)2=4qy.
A variable circle passes through the fixed point A(p,q) and touches x-axis. The locus of the other end of the diameter through A is
Held on 30 Apr 2004 · Verified 6 Jul 2026.
(x−p)2=4qy
(x−q)2=4py
(y−p)2=4qx
(y−q)2=4px
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