Question

The endpoints of a diameter of a circle are ​A(3​,​1) and ​B(8​,13​). Find the area of the circle in terms of pi.

Answer 1

A = 169π/4

Explanation:

From these two given points we find the length of the diameter of this circle, using the Pythagorean Theorem:

d^2 = (8 - 3)^2 + (13 - 1)^2, or

d^2 = 25 + 144 = 169

Thus, the diameter, d, of this circle is √169, or 13.

The radius is thus 13/2 units.

The area formula is A = πr^2. Here the area is

A = π(169/4), or A = 169π/4