 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says does the point minus 2.5, 3.5 lie inside, outside or on the circle x squared plus y squared equal to 25? Before starting the solution let us see this. That says equation of the circle with center at hk and radius r is given by x minus h the whole square plus y minus k the whole square equals to r square. So let us start with the solution to this question. Given equation of the circle is x square plus y square equal to 25 or we can also write it as x minus 0 the whole square plus y minus 0 the whole square equal to 5 square. Now comparing it with the standard equation of the circle that is this we get hk point is equal to 0 0 this is the center and r equal to 5 is the radius of the given circle. Now from this we can see that the circle is having center at the point 0 0 that is the origin. So now what we do is we find distance minus 2.5, 3.5 origin that is 0 0 from the distance formula this one y1 is given by whole square plus y2 minus y1 the whole square on 0 0 and minus 2.5, 3.5 we get distance and this is equal to 5 the whole square where this acts as x1 y1 and this acts as x2 y2 or we can say this acts as x2 y2 and this as x1 y1 that is equal to under the root. Now square of 2.5 is minus 3.5 when minus 3.5 comes out of square we have 3.5 the whole square this minus sign with the square becomes positive so we have plus 3.5 the whole square 18.5 that is approximately equal to 4.3 now this is less than 5 so we see that the distance of the point from origin is less than the radius that was equal to 5 hence we can say that the point lies inside the circle. The question is that the point lies inside the circle I hope that you understood the question and enjoyed the session. Have a good day.