SOLUTION: Find the vertices and foci of the ellipse. {{{ 16x^2 + y^2 = -2y }}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the vertices and foci of the ellipse. {{{ 16x^2 + y^2 = -2y }}}      Log On


   

Question 1007364: Find the vertices and foci of the ellipse.
+16x%5E2+%2B+y%5E2+=+-2y+
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
16x%5E2%2By%5E2%2B2y=0
16x%5E2%2B%28y%5E2%2B2y%2B1%29-1=0
16x%5E2%2B%28y%2B1%29%5E2=1
x%5E2%2F%281%2F16%29%2B%28y%2B1%29%5E2=1

The long axis is vertical and the short axis is horizontal. This is like x%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1.


Your ellipse has center at (0,-1).
Minor vertices are ( -1/4, -1 ) and ( 1/4, -1).
Major vertices are (0,0) and (0,-2).
-
system%28a=1%2Cb=1%2F4%29

(HINT: Each focus will be on the y-axis).
c%5E2=a%5E2-b%5E2, and c is the distance from the center to either focus.