1.

Find the equation of circles determined by the following conditions. Circle passes through origin and cuts off intercepts a and b from the axes.

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SOLUTION :LET the equation of the circle be
`x^2+y^2+2gx+2fy+c=0`
As it passes through the points (a, 0) and (0, 0).
We have c = 0, `a^2 + 2gs = 0`, `B^2 + 2fb = 0`
`therefore` 2g = -a, 2f = -b.
`therefore` Equation of the circle is `x^2 + y^2 -ax - by = 0`


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