Question

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

Answer 1

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.

∴Centre = (0, 0) and radius = 5

Distance between point (–2.5, 3.5) and centre (0, 0)

OP = `sqrt((-2.5 - 0)^2 + (3.5 - 0)^2)`

= `sqrt(6.25 + 12.25)`

= `sqrt18.50`

= 4.3 < 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, point (–2.5, 3.5) lies inside the circle.