Question

Find the general equation of a circle referred to two perpendicular tangents as axes.

Answer 1

Let the equation of the circle be

$x^2+y^2+2gx+2fy+d=0$

From the figure

$-g=-f=\left|r\right|$

$g=f=\sqrt{g^2+f^2-d}$

$g^2=d=f^2$

So, the equation of circle becomes

$x^2+y^2+2gx+2gy+g^2=0$

Let $g=c$

So, the equation becomes

$x^2+y^2+2cx+2cy+g^2=0$