Question

Find the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).

A.

(x - 2)2 + (y - 5)2 = 25

B.

(x - 2)2 + (y - 5)2 = 169

C.

(x + 3)2 + (y + 7)2 = 25

D.

(x + 3)2 + (y + 7)2 = 169




it was B

Answer 1

B

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

The centre is at the midpoint of the diameter ⇒ (2, 5)

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

Calculate r using the distance formula

r = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, - 7) and (x₂, y₂ ) = (2, 5)

r =
`√((2+3)^2+(5+7)^2)` =
`√(25+144)` =
`√(169)` = 13

(x - 2)² + (y - 5)² = 13²

(x - 2)² + (y - 5)² = 169 → B