Question

Write the equation of the directrix of the parabola shown below.y^2+16y+4x+4=0

Answer 1

Answer:

Hello,

F=(14,-8)

directrice: x=16

Step-by-step explanation:

Making reduce form:

$y^2+16y+4x+4=0\\y^2+2*8y+64-64+4x+4=0\\\\(y+8)^2-60+4x=0\\\\x=-\dfrac{(x+8)^2}{4} +15$

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

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