Question 768411
Identify the equation AND the graph of the ellipse with foci at (0, +- 6) and vertices at (0, +- 8)
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This is an ellipse with vertical major axis. (y-coordinates of foci and vertices change but x-coordinates do not.
Its standard form of equation: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
y-coordinate of center=0 (midpoint of foci or vertices)
x-coordinate=0
center: (0,0)
a=8 (distance from center to vertices)
a^2=64
c=6 (distance from center to foci)
c^2=36
c^2=a^2-b^2
b^2=a^2-c^2=64-36=28
Equation:
{{{x^2/28+y^2/64=1}}}
see graph below:
y=±(64-16x^2/7)^.5
{{{ graph( 300, 300, -10, 10, -10, 10, (64-16x^2/7)^.5,-(64-16x^2/7)^.5) }}}