Question

Write the equation of the circle with center (3,-2), and passes through the point (0,2).

Answer 1

Answer:

(x - 3)² + (y + 2)² = 25

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre to a point on the circle

To calculate r use the distance formula

r = √(x₂ - x₁)² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, - 2)

r = $\sqrt{(3-0)^2+(-2-2)^2}$ = $\sqrt{9+16}$ = $\sqrt{25}$ = 5

(x - 3)² + (y + 2)² = 25 ← equation of circle