Question

A circle passes through the point (2,1) and the line x + 2y = 1 is a tangent to it at the point (3,-1) Determine its equation.

Answer 1

The required circle will be
$(x-3{)}^2+(y+1{)}^2+\lambda (x+2y-1)=0$ ......(1)
It passes through (2,1)
$5+3\lambda =0\therefore \lambda =-5/3$
Putting in (1) , the required circle is
$3(x^2+y^2)-23x-4y+35=0$