Question

Determine the equation of the circle graphed below.

( please help me )

Answer 1

(x - 3)² + (y + 5)² = 10

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) = (3, - 5 ) , then

(x - 3)² + (y - (- 5) )² = r² , that is

(x - 3)² + (y + 5)² = r²

r is the distance from the centre to a point on the line

Calculate r using the distance formula

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

with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (6, - 4)

r =
`√((6-3)^2+(-4+5)^2)`

=
`√(3^2+1^2)`

=
`√(9+1)`

=
`√(10)` ⇒ r² = (
`√(10)` )² = 10

(x - 3)² + (y + 5)² = 10 ← equation of circle