Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = - 2

y = `1/8x^2.

Step-by-step explanation:

This is a parabola which opens upwards.

For any point P on the curve the distance of the point from the focus = the perpendicular distance of P  from the directrix.

sqr( x^2 + ( y - 2)^2) = y - (-2)    Squaring both sides:

x^2 + (y - 2)^2 = (y + 2)^2

x^2 + y^2 - 4y + 4 = y^2 + 4y + 4

x^2 - 8y = 0

x^2 = 8y

y = `1/8x^2  (answer).

ok

step-by-step explanation:

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