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Answer:
(x + 1)² + (y - 6)² = 50
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.
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r =
with (x₁, y₁ ) = (- 1, 6) and (x₂, y₂ ) = (- 6, 1)
r =
=
=
=
(h, k ) = (- 1, 6 ), then
(x - (- 1))² + (y - 6)² = ( )² , that is
(x + 1)² + (y - 6)² = 50 ← equation of circle