Math question?

Question

how do you find the coordinates of the foci of an ellipse?

also

how do you write the equation of an ellipse

and parabola?

Answer 1

Ellipse with center at (h,k):
(x-h)^2/a^2 +(y-k)^2/b^2 = 1 major axis || to x-axis
(y-k)^2/a^2 +(x-h)^2/b^2= 1 major axis || to y-axis
2a = length of major axis, 2b = length of minor axis
c=sqrt(a^2-b^2) where c and -c are the foci on the major axis.

Parabola with vertex at (h,k):
(y-k)^2=2p(x-h) axis || to x-axis
(x-h)^2 =2p(y-k) axis || to y-axis
p = distance between focus and directrix and p/2 is distance between focus and vertex.