Does the point (–2.5, 3.5) lie inside, outside or on the circle x² + y² = 25?

Solution:

The equation of the given circle is x² + y² = 25

⇒ x² + y² = 25

⇒ (x - 0)² + (y - 0)² = 5²

which is of the form (x - h)² + (y - k)² = r² , 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

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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 x² + y² = 25 ?

Summary:

The point (- 2.5, 3.5) lies inside the circle x² + y² = 25