Question 848626
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 {{{(x-h)^2 + (y-k)^2  = r^2}}}where (h,k) is the center of the circle. This is not the case.

b) Equation of a hyperbola is {{{((x-h)^2)/a^2 - ((y-k)^2)/b^2 = r^2}}} Close, but this is not subtraction.

c) Equation of an ellipse is {{{((x-h)^2)/a^2 +((y-k)^2)/b^2 = r^2}}} 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^2+bx+c = 0}}}.

<img src = http://www3.wolframalpha.com/Calculate/MSP/MSP78321i29e3816c1gd3400005i1599a8cfdgha4f?MSPStoreType=image/gif&s=3&w=200.&h=114.&cdf=RangeControl />