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) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

step-by-step explanation:

your answer is a