Where is the center of an ellipse for a lithotripsy procedure with an equation of 6.25x^2+16y^2-12.5x+64y-29.75=0?

Question

1. Pick the answer corresponding the coordinates of the ellipse: (A) (-2,1) , (B) (-1,2), (C) (1, -2), (D) (2,1).
2. Pick the answer corresponding to the the coordinates where the shock-wave generator and the patient’s kidney stone (the two foci of the ellipse) should be placed: (A) (1, 3.12) and (1, -3.12) (B) (4.12, 2) and (-2.12, -2) (C) (1, -2) and (-1, -2) (D) (3.12, -2) and (-3.12, -2)
3. Choose either question 1 or question 2 and explain, by listing each step you took, how you found the answer for that question.

Answer 1

1. 6.25(x - 1)² + 16(y + 2)² = 29.75 + 6.25 + 64; (x - 1)²/16 + (y + 2)²/6.25 = 1;

Center at point (1, - 2); answer C)

2.c² = 16 - 6.25 = 9.75; c = 3.12; Foci: F₁ = (-3.12 +1,- 2) = (- 2.12, - 2); F₂ = (3.12 + 1, - 2) = (4.12, - 2)

Answer is B) only they have mistake there