Question

Write the equation of the circle with center (−3, 2) and (6, 4) a point on the circle.

A) (x + 3)2 + (y − 2)2 = 13
B) (x + 3)2 + (y − 2)2 = 25
C) (x + 3)2 + (y − 2)2 = 85
D) (x + 3)2 + (y − 2)2 = 117

Answer 1

C

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, 2), thus

(x + 3)² + (y - 2)² = r²

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

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (6, 4)

r =
`√((6+3)^2+(4-2)^2)`

=
`√(9^2+2^2)` =
`√(85)`

Hence

(x + 3)² + (y - 2)² = (
`√(85)` )², that is

(x + 3)² + (y - 2)² = 85 → C