Answer:
(x - 8)² + (y + 6)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
Here (h, k ) = (8, - 6 ) , then
(x - 8)² + (y - (- 6))² = r² , that is
(x - 8)² + (y + 6)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = ![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%20%20%20%20%7D)
with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )
r = ![\sqrt{(5-8)^2+(-2-(-6))^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%285-8%29%5E2%2B%28-2-%28-6%29%29%5E2%7D)
= ![\sqrt{(-3)^2+(-2+6)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-3%29%5E2%2B%28-2%2B6%29%5E2%7D)
= ![\sqrt{9+4^2}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B4%5E2%7D)
= ![\sqrt{9+16}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B16%7D)
= ![\sqrt{25}](https://tex.z-dn.net/?f=%5Csqrt%7B25%7D)
= 5
Then equation of circle is
(x - 8)² + (y + 6)² = 5² , that is
(x - 8)² + (y + 6)² = 25