MATH SOLVE

5 months ago

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

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