Question

What is the equation of the circle with the given information below?

Center: (-4,7)
Point on Circle: (-1,9). What would be the radius

Answer 1

(x + 4)² + (y - 7)² = 13

Explanation:

Standard equation of a circle is given by,

(x - h)² + (y - k)² = r²

Here, (h, k) is the center and 'r' is the radius of the circle.

If the center of the circle is (-4, 7) and point on the circle is (-1, 9)

Then the length of the radius = Distance between the center and the point lying on the circle

=
`√((-4+1)^2+(7-9)^2)`

=
`√(9+4)`

=
`√(13)`

Therefore, equation of the circle will be,

(x + 4)² + (y - 7)² =
`(√(13))^2`

(x + 4)² + (y - 7)² = 13