Question

Select the correct answer.
What is the equation of the parabola shown in the graph?

Answer 1

x=y2/8+y/2+9/2

Explanation:

Given:

directrix: x=2

focus = (6,-2)

Standard equation of parabola is given by:

(y - k)2 = 4p (x - h)

where

directrix : x=h-p

focus=(h + p, k)

Now comparing the give value with above:

(h + p, k)= (6,-2)

k=-2

h+p=6

h=6-p

Also

directrix: x=h-p

h-p=2

Putting value of h=6-p in above

6-p-p=2

6-2p=2

-2p=2-6

-2p=-4

p=-4/-2

p=2

Putting p=2 in h-p=2

h=2+p

h=2+2

h=4

Putting k=-2, p=2, h=4 in standard equation of parabola we get:

(y - k)2 = 4p (x - h)

(y-(-2))^2 = 4(2) (x - 4)

(y+2)^2 = 8 (x - 4)

y2+4y+4=8x-32

y2+4y+4+32=8x

x=y2/8+4y/8+36/8

x=y2/8+y/2+9/2!