Question

Find the equation of the circle which touches the axes and whose' centre lies on x - 2y = 3.

Answer 1

The required circle touches A(a, 0) and 13(0, a) on the axes
so the centre = (a, a)P, radius = a
Also, the centre lies on x - 2y = 3 a = 3
$\Rightarrow a-2a=3\Rightarrow -a=3\Rightarrow a=-3$
$\therefore$ centre =(-3,-3) and radius =3
Thus the equation of circle is
$(x+3{)}^2+(y+3{)}^2=3^2\Rightarrow x^2+y^2+6x+6y+9=0$