Question

Does the point $(-2.5,3.5)$ lie inside outside or on the circle $x^2+y^2=25$?

Answer 1

The equation of the given circle is $x{}^2+y{}^2=25$
$\Rightarrow$ Centre $=(0,0)$ and radius $=5$
Distance between point $(-2.5,3.5)$ and centre $(0,0)$
$=\sqrt{{(-2.5-0)}^2+{(3.5-0)}^2}$

$=\sqrt{6.25+12.25}=\sqrt{18.5}=4.3\text{(approx)}<5$

Since the distance between point $(-2.5,3.5)$ and centre $(0,0)$ of the circle is less than the radius of the circle.
Hence the point $(-2.5,3.5)$ lies inside the circle.