Answer:
B
Step-by-step 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 = [tex]\sqrt{(-3-2)^2+(-7-5)^2}[/tex]
= [tex]\sqrt{(-5)^2+(-12)^2}[/tex]
= [tex]\sqrt{25+144}[/tex] = [tex]\sqrt{169}[/tex] = 13, hence
(x - 2)² + (y - 5)² = 13², thus
(x - 2)² + (y - 5)² = 169 → B
