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 = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (5, - 2 )
r = [tex]\sqrt{(5-0)^2+(-2-2)^2}[/tex]
= [tex]\sqrt{5^2+(-4)^2}[/tex]
= [tex]\sqrt{25+16}[/tex]
= [tex]\sqrt{41}[/tex] , then r² = ([tex]\sqrt{41}[/tex] )² = 41
then
(x - 0)² + (y - 2)² = 41 , that is
x² + (y - 2)² = 41 ← equation of circle
