SOLUTION: This is a multiple choice question. The graph of the equation {{{4x^2 + 16y^2 = 25}}} is; a. a circle, b. a hyperbola, c. an ellipse, d. a parabola Choice a. and b. are ruled ou

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: This is a multiple choice question. The graph of the equation {{{4x^2 + 16y^2 = 25}}} is; a. a circle, b. a hyperbola, c. an ellipse, d. a parabola Choice a. and b. are ruled ou      Log On


   



Question 848626: This is a multiple choice question. The graph of the equation 4x%5E2+%2B+16y%5E2+=+25 is; a. a circle, b. a hyperbola, c. an ellipse, d. a parabola
Choice a. and b. are ruled out.

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
I know you ruled out a and b. I just want to explain why they are ruled out for future viewers.
a) Equation of a circle is %28x-h%29%5E2+%2B+%28y-k%29%5E2++=+r%5E2where (h,k) is the center of the circle. This is not the case.
b) Equation of a hyperbola is %28%28x-h%29%5E2%29%2Fa%5E2+-+%28%28y-k%29%5E2%29%2Fb%5E2+=+r%5E2 Close, but this is not subtraction.
c) Equation of an ellipse is %28%28x-h%29%5E2%29%2Fa%5E2+%2B%28%28y-k%29%5E2%29%2Fb%5E2+=+r%5E2 This is correct with h = 0, k =0 , r= 5 , a = (1/2) and b = (1/4). <---- ANS
d) A parabola is simply another name for a quadratic ax%5E2%2Bbx%2Bc+=+0.