# How do you find the equation for a circle that passes through the origin and has intercepts equal to 1 and 2 on the x- and y- axes?

Apr 5, 2016

${x}^{2} + {y}^{2} - x - 2 y = 0$.
Let the equation be ${x}^{2} + {y}^{2} + 2 g x + 2 f y + c = 0$.
So, c = 0, g = $- \frac{1}{2}$ and $f = - 1$
Answer: ${x}^{2} + {y}^{2} - x - 2 y = 0$.