# Does the point (–2.5, 3.5) lie inside, outside or on the circle x^{2} + y^{2} = 25?

**Solution:**

The equation of the given circle is x^{2} + y^{2} = 25

⇒ x^{2} + y^{2} = 25

⇒ (x - 0)^{2} + (y - 0)^{2} = 5^{2}

which is of the form (x - h)^{2} + (y - k)^{2} = r^{2} , where h = 0, k = 0 and r = 5

Therefore,

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

= √18.25

= 4.272

Here, 4.272 < 5, which means less than the radius.

Since the distance between the point (- 2.5, 3.5) and center (0, 0) of the circle is less than the radius of the circle, hence, the point (- 2.5, 3.5) lies inside the circle

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.1 Question 15

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

**Summary:**

The point (- 2.5, 3.5) lies inside the circle x^{2} + y^{2} = 25