Question

Provide the standard “equation of the circle” if the center of the circle is located at (2,9) and you have a point on the circle at (2,6)

Answer 1

(x - 2)² + (y - 9)² = 9

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 = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (2, 6)

r =
`√((2-2)^2+(6-9)^2)`

=
`√(0^2+(-3)^2)`

=
`√(0+9)` =
`√(9)` = 3

Centre = (h, k) = (2, 9) and r = 3, thus equation of circle is

(x - 2)² + (y - 9)² = 9