Write the equation for a parabola with a focus at (2, 2) and a directrix at x = 8.

Let  P(x,y) be a point on the parabola.  The definition of a parabola is the squared distance from P to focus F(2,2) equals the squared distance to the directrix x=8.

squared distance from P(x,y) to focus F(2,2)

(x - 2)² + (y - 2)²

squared distance from P(x,y) to the directrix x=8.

(x-8)²

Those are equal in a parabola,

(x - 2)² + (y - 2)² = (x-8)²

x² - 4x + 4 + y² - 4y + 4 = x² - 16x + 64

y² - 4y - 46 = -12x

That's a sideways parabola,

x = -(y² - 4y - 46)/12

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!