Thank you for reporting, we will resolve it shortly
Q.
The equation of the circle passing through the point $(2,1)$ and touching $y$-axis at the origin is
Conic Sections
Solution:
We have the equation of circle
$x^2+y^2+2 g x+2 f y+c=0$
But it passes through $(0,0)$
and $(2,1)$, then
$ c=0 .....$(i)
$ 5+4 g+2 f=0.....$(ii)
As it touches $y$-axis
$\therefore 2 \sqrt{ f ^2- c }=0 [\because c =0]$
or $f=0$, from (ii),$g=-\frac{5}{4}$
