Question

Use the information provided to write the equation of the circle Center: (10,-9) Point on Circle: (12,-13)

Answer 1

Answer:

(x - 10)² + (y + 9)² = 20

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 ) = (10, - 9) and (x₂, y₂ ) = (12, - 13)

r = $\sqrt{(12-10)^2+(-13+9)^2}$

  = $\sqrt{4+16}$ = $\sqrt{20}$, hence

(x - 10)² + (y - (- 9))² = ($\sqrt{20}$)², that is

(x - 10)² + (y + 9)² = 20