Question

A circle is drawn with origin as the center and radius 10 units. Show that the point (–8, –6) is a point on the circle. Find out whether the point (9, –1) lies within the circle or outside the circle. Why?

Answer 1

The distance between the centre and the point (-8,-6) is = \(\sqrt{(-8)^2+(-6)^2}\)

= \(\sqrt{100}\) = 10

It is equal to the radius. So the point (-8, -6) is a point on the circle.

The distance between the centre, and the point (9,-1) is = \(\sqrt{9^2+(-1)^2}\)

= \(\sqrt{81+1}\) = \(\sqrt{82}\)

√82 is smaller than 10.

So the point (9, –1) is a point inside the circle.

Distance between (x₁, y₁) and (x₃, y₂) is

\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance of (x, y) from (0, 0) is \(\sqrt{x^2+y^2}\)