Answer:
(x + 5)² + (y + 7)² = 288
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 (- 5, - 7) to the point on the circle (7, 5)
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)
r = [tex]\sqrt{(7+5)^2+(5+7)^2}[/tex] = [tex]\sqrt{12^2+12^2}[/tex] = [tex]\sqrt{288}[/tex]
Hence
(x - (- 5))² + (y - (- 7))² = ([tex]\sqrt{288}[/tex])², that is
(x + 5)² + (y + 7)² = 288
