Question

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

Answer 1

Answer:

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

Step-by-step 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?

$\frac{3A}{4} = \frac{3*64\pi}{4} = 3*16\pi = 48\pi$

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