Q:

In the coordinate plane, a circle has center (2,−3) and passes through the point (5,0). what is the area of the circle?

Accepted Solution

A:
Find the radius (or you can find the square of the radius)
the general equation for a circle is
(x - a)² + (y - b)² = r²
with (a,b) as the center, and (x,y) is one of the points

plug in the numbers to the equation to find the value of r
(x - a)² + (y - b)² = r²
(5 - 2)² + (0 - (-3))² = r²
3² + (0 + 3)² = r²
3² + 3² = r²
2(3²) = r²
r² = 2(3²)
r² = 2(9)
r² = 18

Find the area of the circle
a = π × r²
a = 3,14 × 18
a = 56.52

The area of the circle is 56.52 square unit