Question

Find an equation of the circle that satisfies the given conditions. Center (−2, 10); passes through (9, 7)

Answer 1

(x + 2)² +(y - 10)² = 130

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

given (h, k ) = (- 2, 10 ) we require to find r

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

given the circle passes through (9, 7 )

calculate the radius using the distance formula

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

let (x₁, y₁ ) = (- 2, 10 ) and (x₂, y₂ ) = (9, 7 )

substitute these values into the formula for r

r =
`√((9-(-2))^2+(7-10)^2)`

=
`√(9+2)^2)+(-3)^2`

=
`√(11^2+9)`

=
`√(121+9)`

=
`√(130)`

then the equation of the circle is

(x - (- 2) )² + (y - 10)² = (
`√(130)` )² , that is

(x + 2)² + (y - 10)² = 130 ← equation of circle