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]