Question

99 POINTS!!! Find the equation for an ellipse with vertices at (-6, 0) and (6, 0) and foci at (-4, 0) and (4, 0).

Answer 1

(x^2)/a^2+(y^2)/b^2=1
a>b
a=6, a^2=36
foci=(a^2-b^2)^(1/2)
4=(36-b^2)^(1/2)
16=36-b^2
b^2=36-16
b^2=20
b=2(5)^(1/2) or (20)^(1/2)
1=(x^2/36)+(y^2/20)

Answer 2

(x^2)/a^2+(y^2)/b^2=1

a>b

a=6, a^2=36

foci=(a^2-b^2)^(1/2)

4=(36-b^2)^(1/2)

16=36-b^2

b^2=36-16

b^2=20

b=2(5)^(1/2) or (20)^(1/2)

1=(x^2/36)+(y^2/20)