Question

What is the equation of the circle shown?

Answer 1

(x + 4)² + (y - 2)² = 8

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

Here (h, k ) = (- 4, 2 ) , then

(x - (- 4))² + (y - 2)² = r²

(x + 4)² + (y - 2)² = r²

CA is the radius of the circle

To find r use the distance formula

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

with (x₁, y₁ ) = C(- 4, 2) and (x₂, y₂ ) = A(- 2, 4)

r =
`√((-2+4)^2+(4 -2)^2)`

=
`√(2^2+2^2)`

=
`√(8)` , then r² = (
`√(8)` )² = 8

Then

(x + 4)² + (y - 2)² = 8 ← equation of circle