Find the equation of there circal passing through (0,0)and moving intercepts a and b on the coordinate axis
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A general equation of a circle is
$
x^2+y^2+2 g x+2 f y+c=0
$
Since it passes through $(0,0)$,
$
c=0
$
So the equation becomes
$
x^2+y^2+2 g x+2 f y=0
$
It cuts the x -axis at ( $a, 0$ ).
Substituting:
$
a^2+2 g a=0
$
g=-a/2
It cuts the y -axis at $(0, b)$.
Substituting:
$
b^2+2 f b=0 \Rightarrow f=-\frac{b}{2}
$
Putting values of $g$ and $f$ :
$
x^2+y^2-a x-b y=0
$
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