How do you find the equation of an ellipse with vertices #(+-5,0)# and foci #(+-2,0)#?

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Answer 1 · 2017-11-27T03:10:15

#x^2/25 + y^2/21 =1#

Given an ellipse with centre at the origin and with foci at the points #F_{1}=(c,0) and F_{2}=(-c,0)#

and vertices at the points
#V_{1}=(a,0) and V_{2}=(-a,0)#

The equation of the ellipse will satisfy:

#x^2/a^2 + y^2/(a^2-c^2)=1#

In our example; #a=5 and c=2#

Hence. #x^2/5^2 + y^2/(5^2-2^2)=1#

#x^2/25 + y^2/(25-4) =1#

#x^2/25 + y^2/21 =1#

We can see this ellipse on the graph below.

graph{ x^2/25 + y^2/21 =1 [-16.01, 16.02, -8.01, 8]}