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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

2

step-by-step explanation:

1+1=2

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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