Write the equation of a parabola whose directrix is y=9.75 and has a focus at (8, 0.25).

y = (-1/19)(x - 8)² + 1521/76

Step-by-step explanation:

A parabola moves in such a way that it's distance from it's focus and directrix are always equal.

Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4

If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;

√((x - 8)² + (y - ¼)²)

Distance from that point to the directrix is; (y - 39/4)

Thus;

√((x - 8)² + (y - ¼)²) = (y - 39/4)

Taking the square of both sides gives;

((x - 8)² + (y - ¼)²) = (y - 39/4)²

(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²

Simplifying this gives;

(x - 8)² - (39/4)² = (½ - 39/2)y

(x - 8)² - 1521/4 = -19y

(x - 8)² - 1521/4 = -19y

Divide both sides by -19 to get;

y = (-1/19)(x - 8)² + 1521/76

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

7,24

step-by-step explanation: