Question

Determine the equation of the circle graphed below.

-12-11-10-9-8-7 -5-4-3-2
11098765432-
hadis
-2
-9
-10
-11
123456
8 9 10 11 12
(8,-2)

Answer 1

(x - 3)² + (y + 4)² = 29

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

we have the coordinates of the centre but require to find the radius r

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

using the distance formula to find r

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

with (x₁, y₁ ) = (3, - 4 ) centre and (x₂, y₂ ) = (8, - 2) point on circle

r =
`√((8-3)^2+(-2-(-4))^2)`

=
`√(5^2+(-2+4)^2)`

=
`√(25+2^2)`

=
`√(25+4)`

=
`√(29)`

then equation with centre (3, - 4 ) and r =
`√(29)` , is

(x - 3)² + (y - (- 4) )² = (
`√(29)` )² , that is

(x - 3)² + (y + 4)² = 29