Question

Find the equation of the parabola with its focus at (–5,0) and its directrix y = 2.

Options:

A)

y = 1∕4(x + 5)^2 + 1

B)

y = –4(x + 5)^2 + 1

C)

y = –1∕4(x + 1)^2 + 5


D)

y = –1∕4 (x + 5)^2 + 1

Answer 1

2 = 1

Explanation:

5y = ax + 5 and 1/4y = 1/10x - 1We need both formula in slope-intercept format...y=mx+bm=slopeb=y-intercept, value of y when x=05y = ax + 5Let's divide both sides by 5...(5y)/5=[(a/5)x]+(5/5)y=(a/5)x+1Any line parallel to this, must have a slope equal to a/5. 1/4y = 1/10x - 1Let's multiply both sides by 4...4[(1/4)y]=[(1/10)(4)x]-[(1)(4)]y=(4/10)x-4y=(2/5)x-4 2/5 = a/5 2=a