Question

A circle has an equation (x+2)2+(y−5)2=64. What is 34 of its area.

Answer 1

3/4 of the area of the circle is of
`48\pi` squared units.

Explanation:

Equation of a circle:

The equation of a circle has the following format:

`(x - x_0)^2 + (y - y_0)^2 = r^2`

In which the center is
`(x_0,y_0)` and r is the radius.

Area of a circle:

The area of a circle of radius r is given by:

`A = \pi r^2`

Circle (x+2)² + (y-5)² = 64

Comparing with the standard equation, we have that:

`r^2 = 64`

Area of the circle:

`A = \pi r^2 = 64\pi`

What is 3/4 of its area?

`(3A)/(4) = (3*64\pi)/(4) = 3*16\pi = 48\pi`

3/4 of the area of the circle is of
`48\pi` squared units.