Answer:
(x - 4)² + (y + 7)² = 53
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 =
=
=
=
Hence r² = (
)² = 53
(x - 4)² + (y + 7)² = 53 ← equation of circle