Question

Write the equation of the directrix of the parabola shown below.

y^2+16y+4x+4=0

Answer 1

Hello,

F=(14,-8)

directrice: x=16

Explanation:

Making reduce form:

`y^2+16y+4x+4=0\\y^2+2*8y+64-64+4x+4=0\\\\(y+8)^2-60+4x=0\\\\x=-((x+8)^2)/(4) +15\\`

Since i prefere working with y=...: exchanging x and y

`y=-((x+8)^2)/(4) +15\\\\Comparing\ to\ y=((x-a)^2)/(2(b-k)) +(b+k)/(2) \\\\a=-8 :\ S=(-8,15)\\\\\\b-k=-2\ and\ b+k=30 \ \longrightarrow\ b=14\ and\ k=16\\\\Exchanging\ x\ and\ y:\\\\Focus=(14,-8)\\\\x=16`