Question

Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinates axes.

Answer 1

The circle makes intercepts a with x axis and b with y - axis.
$\therefore OA=aandOB=b$
So the co-ordinates of A are (a,0) and B are (0,b) Now the cirlce passes through three points O(0,0), A (a, 0) and B (0,b).

Putting the co-ordinates of three point in the point in teh equation of circle
$x^2+y^2+2gx+2fy+c=0c=0a^2+2ga=0\Rightarrow a(a+2g)=0\Rightarrow g=\frac{-1}{2}a{b}^2+2fb=0\Rightarrow b(b+2f)=0\Rightarrow f=\frac{-1}{2}b\text{Putting these values of g,f and c in (i), We have}{x}^2+y^{+}2\times \frac{-1}{2}ax+2\times \frac{-1}{2}by+0=0\Rightarrow x^2+y^2-ax-by=0$
Which is required equation of circle.