How do you write an equation for an ellipse given endpoints of the major axis at (0,10) and (0,-10) and foci at (0,8) and (0,-8)?

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Answer 1 · 2018-01-09T13:02:20

The equation of ellipse is $x^2/36+y^2/100=1$

Semi major axis is $a=10$ and focus $c=8$ from the centre

$(0,0)$ . This is vertical ellipes of which the equation is

$x^2/b^2+y^2/a^2=1 or x^2/b^2+y^2/10^2=1$

c is the distance from the center to a focus. The relation of

$c, a, b$ is $c^2 = a^2 - b^2:. 8^2=10^2-b^2$ or

$b^2=100-64=36 :b= 6$

Hence the equation of ellipse is $x^2/6^2+y^2/10^2=1$ or

$x^2/36+y^2/100=1$

graph{(x^2/36+y^2/100)=1 [-40, 40, -20, 20]} [Ans]