Question

A circle with centre ‘P’ touches the x - axis and also touches the circle with centre (0, 3) and radius 2. The locus of ‘P’ is a conic whose length of semi latus rectum is ___

Answer 1

Centre = P (h , k), radius = k
$C_1{C}_2=r_1+r_2$
$\Rightarrow \sqrt{h^2+(k-3{)}^2}=k+2$
$\Rightarrow h^2-10k+5=0$
$\therefore$ Locus of P is $x^2=10y-5=10(y-\frac{1}{2})$