Question

Find the equation of the circle, the end points of whose diameter are $(2,-3)$ and $(-2,4)$. Find the centre and radius.

Answer 1

Diametric end points $-$ $(2,-3)$ and $(-2,4)$

centre at $(\frac{2+2}{2},\frac{-3+4}{2})$

$(2,\frac{1}{2})$

Radius $=\sqrt{(2-2{)}^2+{(-3-\frac{1}{2})}^2}$

$=\sqrt{0+\frac{49}{4}}=\frac{7}{2}$

Equation$-$ $(x-2{)}^2+(y-\frac{1}{2}{)}^2={\left(\frac{7}{2}\right)}^2$

$(x-2{)}^2+(y-\frac{1}{2}{)}^2=\frac{49}{4}$.