Answer:
D
Step-by-step explanation:
Obtain the equation of the circle in standard form
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 13, - 12), thus
(x + 13)² + (y + 12)² = r²
The radius is the distance from the centre (- 13, - 12) to the point on the circumference (- 17, - 12)
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 17, - 12) and (x₂, y₂ ) = (- 13, -12)
r = [tex]\sqrt{(-13+17)^2+(-12+12)^2}[/tex] = [tex]\sqrt{16}[/tex] = 4
Hence
(x + 13)² + (y + 12)² = 16 ← in standard form
Substitute the coordinates of each point into the left side of the equation and check
A (- 17, - 13) : (- 4)² + (- 1)² = 16 + 1 = 17 ≠ 16
B (- 9, - 17) : 4² + (- 5)² = 16 + 25 = 41 ≠ 16
C (- 12, 13) : 1² + 25² ≠ 16
D (- 9, - 12) : 4² + 0² = 16
Since (- 9, - 12) satisfies the equation, it is on the circle → D
