Question

What is the directrix of the parabola defined by 14(y+3)=(x−2)2?

Answer 1

HI!!

Answer 2

you need the vertex first
do you know it?q

Answer 3

just asking
if not, say so and i will tell you

Answer 4

no

Answer 5

ok it looks like \[4p(y-k)=(x-h)^2\] has center \((h,k)\)so your center is \((2,-3)\)

Answer 6

is that the directrix

Answer 7

no that is the vertex, we need that first so we can find the directrix

Answer 8

okay

Answer 9

\[4p=14\] so \[p=\frac{14}{4}=\frac{7}{2}\] that means the directrix is \(\frac{7}{2}\) units down from \((2,-3)\)

Answer 10

so then it would just be 7/2

Answer 11

no, 7/2 units below \((2,-3)\) that is why we needed the vertex first q

Answer 12

\[-3-\frac{77}{2}=-\frac{13}{2}\] the directrix is \[y=-\frac{13}{2}\]

Answer 13

oh and the directix is a horizontal line, not a number so it is the equation \[y=-\frac{13}{2}\]