which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?
x squared over 4 plus y squared over 1 equals 1
x squared over 2 plus y squared over 1 equals 1
x squared over 1 minus y squared over 4 equals 1
x squared over 1 minus y squared over 2 equals 1

Step-by-step explanation:

It was given that, the ellipse has directrices at

The directrices has equation: , where is the eccentricity of the ellipse.

eqn(1)

The foci are at: (0,1) qnd (0,-1)

Also, the foci are given by:

eqn(2)

Solving equation (1) and (2) simultaneously we get;

and

We use the relation, to get:

.

The equation of the ellipse is given by:

We substitute the values to get:

Or

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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