Question 516974: an ellipse has a vertex at (1,0) a co vertex at (0,4) and a center at the origin which is the equation of the ellipse in standard form? Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! an ellipse has a vertex at (1,0) a co vertex at (0,4) and a center at the origin which is the equation of the ellipse in standard form?
**
Given coordinates of vertices shows this is an equation of an ellipse with vertical major axis of the standard form: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.
For given equation:
center: (0,0) (given)
b=1
b^2=1
a=4
a^2=16
..
Equation:
x^2/1+y^2/16=1
see graph below as a visual check on the answer.
..
y=±(16-16x^2)^.5
(