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)

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.