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which is the equation of an ellipse with directrices at y = ±4 and foci at (0, 2) and (0, −2)?

x squared over 16 minus y squared over 4 equals 1
x squared over 4 plus y squared over 16 equals 1
x squared over 8 minus y squared over 4 equals 1
x squared over 4 plus y squared over 8 equals 1

Step-by-step explanation:

we know that

The ellipse has directrices at > given

The directrices has equation:

where e is the eccentricity of the ellipse.

so

> equation A

Remember that the foci are given by:

In this problem

The foci are at (0,2) and (0,-2)

so

> equation B

Solve the system of equations A and B

substitute equation A in equation B

Find the value of a

We know,

Substituting the values, we get

The equation of the ellipse is given by:

we have

substitute

therefore

x squared over 4 plus y squared over 8 equals 1

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

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part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: