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Answer:
(x + 4)² + (y - 2)² = 8
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, 2 ) , then
(x - (- 4))² + (y - 2)² = r²
(x + 4)² + (y - 2)² = r²
CA is the radius of the circle
To find r use the distance formula
r =
with (x₁, y₁ ) = C(- 4, 2) and (x₂, y₂ ) = A(- 2, 4)
r =
=
= , then r² = (
)² = 8
Then
(x + 4)² + (y - 2)² = 8 ← equation of circle