What is the equation of the parabola with focus(1, 1/2)
and directrix y = 3?
A. Y=x^2+17x-1
B. Y=-3/16x^2
C. Y=1/5x^2+2/5x+31/20
D. Y=-3/5x^2-14/31x+71/16

Given:

Focus of a parabola =

Directrix:

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

           ...(A)

Where, is center, is focus and is the directrix.

On comparing the focus, we get

          ...(i)

On comparing the directrix, we get

             ...(ii)

Adding (i) and (ii), we get

Putting is (i), we get

Putting in (A), we get

On further simplification, we get

Therefore, the equation of the parabola is .

Note: Option C is correct but the leading coefficient should be negative.

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