Answer:
(x - 4)² + (y + 7)² = 53
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) = (4, - 7), so
(x - 4)² + (y + 7)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 ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)
r = [tex]\sqrt{(-3-4)^2+(-5+7)^2}[/tex]
= [tex]\sqrt{(-7)^2+2^2}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]
Hence r² = ([tex]\sqrt{53}[/tex] )² = 53
(x - 4)² + (y + 7)² = 53 ← equation of circle
