Answer:
(x + 5)² + (y + 8)² = 49
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) = (- 5, - 8), so
(x - (-5))² + (y - (- 8))² = r², that is
(x + 5)² + (y + 8)² = r²
The radius is the distance from the centre to a point on the circle
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, - 8) and (x₂, y₂ ) = (2, - 8)
r = [tex]\sqrt{(2+5)^2+(-8+8)^2}[/tex] = [tex]\sqrt{7^2+0^2}[/tex] = [tex]\sqrt{49}[/tex] = 7
r = 7 ⇒ r² = 7² = 49
Hence
(x +5)² + (y + 8)² = 49 ← equation of circle
