Question

Find whether the point $(1;\frac{\sqrt{11}+6}{6})$ lies inside or outside the circle whose equation is $3x^2+3y^2-5x-6y+4=0$. Find its centre and radius.

Answer 1

Dividing by 3, we get the circle as C$(\frac{5}{6},1)$, r = $\frac{1}{6}\sqrt{13}$
and given point is P.
P will be outside, on or inside the circle according as
CP${}^2$ >, = or < r${}^2$. But CP${}^2$ = $\frac{12}{36}<\frac{13}{36}$= r${}^2$.
Since CP${}^2$ < r${}^2$, the point P is inside the circle.