Question

Determine the equation of the circle with center (0, -5) containing the point
(-√60,-6).

Answer 1

x² + (y + 5)² = 61

Explanation:

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b ) are the coordinates of the centre and r is the radius

here (a, b ) = (0, - 5 ) and r has to be found

(x - 0)² + (y - (- 5) )² = r² , that is

x² + (y + 5)² = r²

the radius is the distance from the centre to a point on the circle.

using the distance formula to find r

r =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (0, - 5 ) and (x₂, y₂ ) = (-
`√(60)` , - 6 )

r =
`\sqrt{(-√(60)-0)^2+(-6-(-5))^2 }`

=
`\sqrt{(-√(60))^2+(-1)^2 }`

=
`√(60+1)`

=
`√(61)`

then r² = (
`√(61)` )² = 61

the equation of the circle is then

x² + (y + 5)² = 61