Question

A variable circle passes through the points $P(1,2)$ and touches the x-axis. The locus of the other end of the diameter through $P$ is

Answer 1

eqn of circle $\to$

$(x-1)(x-h)+(y-2)(y-k)=0$

$x^2+y^2-(h+1)x-(b+2)y+h+2b=0$

Since, the circle touches the $x-axis$

$g^2=c$

${\left(\frac{h+1}{2}\right)}^2=(h+2b)$

$(x+1{)}^2=4(x+2y)$