Question

What is the answer to this? is it D​

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 midpoint of the diameter is the centre of the circle, hence

(h, k) = (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 ) = (2, 5) and (x₂, y₂ ) = (- 3, - 7)

r =
`√((-3-2)^2+(-7-5)^2)`

=
`√((-5)^2+(-12)^2)`

=
`√(25+144)` =
`√(169)` = 13, hence

(x - 2)² + (y - 5)² = 13², thus

(x - 2)² + (y - 5)² = 169 → B