Answer:
x² + (y - 2)² = 41
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 distance from the centre to a point on the circle is the radius r
calculate r using the distance formula
r =
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (5, - 2 )
r =
=
=
= , then r² = ( )² = 41
then
(x - 0)² + (y - 2)² = 41 , that is
x² + (y - 2)² = 41 ← equation of circle