Class 11

Math

3D Geometry

Conic Sections

Does the point $(−2.5,3.5)$ lie inside outside or on the circle $x_{2}+y_{2}=25$?

The equation of the given circle is $x_{2}+y_{2}=25$

$⇒$ Centre $=(0,0)$ and radius $=5$

Distance between point $(−2.5,3.5)$ and centre $(0,0)$

$=(−2.5−0)_{2}+(3.5−0)_{2} $

$=6.25+12.25 =18.5 =4.3(approx)<5$

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.

$⇒$ Centre $=(0,0)$ and radius $=5$

Distance between point $(−2.5,3.5)$ and centre $(0,0)$

$=(−2.5−0)_{2}+(3.5−0)_{2} $

$=6.25+12.25 =18.5 =4.3(approx)<5$

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.