Question 552799: Graph the equation. Identify the vertices, co vertices, and foci of the ellipse.
{[(x^2)/16]+[(y^2)/4]}=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Graph the equation. Identify the vertices, co vertices, and foci of the ellipse.
{[(x^2)/16]+[(y^2)/4]}=1
**
(x^2)/16+(y^2)/4=1
This is an equation for an ellipse with horizontal major axis. Its standard form:
y=(x-h)^2/a^2+(y-k)^2/b^2, a>b, with (h,k) being the (x,y) coordinates of the center.
For given equation:
Center: (0, 0)
a^2=16
a=√16=4
b^2=4
b=2
c^2=a^2-b^2=16-4=12
c=(x^2)/16]+[(y^2)/4]}=√12≈3.46
..
vertices: (0±a,0)=(0±4,0)=(-4,0) and (4,0)
Co-vertices: (0,0±b)=(0,0±2)=(0,-2) and (0,2)
Foci:(0±c,0)=(0±√12,0)=(-3.46,0) and (3.46,0)
see graph below:
..
y=±(4-x^2/4)^.5
|
|
|
