Question

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?

• A. $(x-p{)}^2=4qy$
• B. $(x-q{)}^2=4py$
• C. $(y-p{)}^2=4qx$
• D. $(y-q{)}^2=4px$

Answer 1

The correct option is A $(x-p{)}^2=4qy$

$\Rightarrow (h-p{)}^2+(k-q)=4{\left(\frac{k+q}{2}\right)}^2$
$=k^2+2kq+q^2$
$\Rightarrow (x-p{)}^2=4qy$.