Write the standard form of the equation of the circle with center (-5,-7) that passes through the point (7,5).

Answer:(x + 5)² + (y + 7)² = 288Step-by-step explanation:The equation of a circle in standard form is(x - h)² + (y - k)² = r²where (h, k) are the coordinates of the centre and r is the radiusThe radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)Use the distance formula to calculate rr = √ (x₂ - x₁ )² + (y₂ - y₁ )²with (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