Question

The equation of a circle passing through $(3,-6)$ and touching both the axes is

• A. $x^2+y^2-6 x+6 y+9=0$
• B. $x^2+y^2+6 x-6 y+9=0$
• C. $x^2+y^2+30 x-30 y+225=0$
• D. $x^2+y^2+30 x+30 y+225=0$

Answer 1

Answer: (A)

Now
$ (r-3)^2+(-r+6)^2=r^2 $
$ r^2-18 r+45=0 $
$ \Rightarrow r=3,15$
Hence circle

$(x-3)^2+(y+3)^2=3^2$
$x^2+y^2-6 x+6 y+9=0$
$(x-15)^2+(y+15)^2=(15)^2$
$\Rightarrow x^2+y^2-30 x+30 y+225=0$