Question

The equation of the circle whose diameters have the end points (a,0) and (0,b).

Answer 1

REF.Image

$O\equiv [\frac{O+a}{2},\frac{O+b}{2}]$ $O\equiv (\frac{a}{2},\frac{b}{2})$

Radius = $\sqrt{(a-\frac{a}{2}{)}^2+(\frac{b}{2}{)}^2}$

$=\sqrt{\frac{a^2}{4}+\frac{b^2}{4}}=\sqrt{\frac{a^2+b^2}{4}}=\frac{\sqrt{a^2+b^2}}{2}$

$E{q}^n(x-\frac{a}{2}{)}^2+(y-\frac{b}{2}{)}^2=\frac{a^2+b^2}{4}$