Question

A circle
drawn with origin as the centre passes through $\left(\frac{5}{2},0\right)$ . Does the point $\left(\frac{5}{2},\frac{5}{2}\right)$ lies in
its interior or exterior ?

Answer 1

R.E.F image

To,check if $(\frac{5}{2},\frac{5}{2})$ lies in its

interior or exterior.

$E{q}^n$. of circle : $x^2+y^2=(\frac{5}{2}{)}^2$

$\Rightarrow x^2+y^2=\frac{25}{4}...\left(1\right)$

Put $x=\frac{5}{2},y=\frac{5}{2}$ in eq.(1)

$(\frac{5}{2}{)}^2+(\frac{5}{2}{)}^2=\frac{25}{4}+\frac{25}{4}=\frac{50}{4}\ne \frac{25}{4}$

Since $\frac{50}{4}-\frac{25}{4}=\frac{25}{4}>0$

$\therefore$ Point lies in exterior of the circle