Respuesta :
The equation of the ellipse will be x² / 36 – y² / 32 = 1.
What is an ellipse?
An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.
This ellipse is centered at the origin.
Vertices: (0,-6) (0,6)
Foci: (0,-2) (0,2)
Then the equation of the ellipse will be given as
x² / a² – y² / b² = 1
Let c be the distance between the origin to foci.
Then we have
c = 2
And the value of a will be
a = 6
Then the value of a² will be
a² = 6² = 36
The value of b is the distance from center to one of the Co-vertices. Then the value of b² will be
a² – b² = c²
36 – b² = 2²
b² = 36 – 4
b² = 32
Then the equation of the ellipse will be x² / 36 – y² / 32 = 1.
More about the ellipse link is given below.
https://brainly.com/question/19507943
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