Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = − one half . (2 points) f(x) = −(x + 2)2 − three fourths f(x) = (x + 2)2 + three fourths f(x) = −(x − 2)2 + three fourths f(x) = −(x − 2)2 − three fourths

Step-by-step explanation:

The parabola must have all the points to be equally distant from the point of focus and the directrix, where directrix a horizontal line and the focus being a point given.

To derive an equation for the parabola, we will use the formula of distance. Now we have a random point on the parabola (x,y) and the point (x,y) will be equidistant from the focus and the directrix. So using the distance formula, we will get:

The square root of y-(-1/2) from the directrix, and the righthand side of the equal sign is derived from the focus point. Now simplify it to get:

.

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

what is the graph

step-by-step explanation: