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

Question

misty1212 · Answer

HI!!

misty1212 · Answer

you need the vertex first
do you know it?q

misty1212 · Answer

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

anonymous · Answer

no

misty1212 · Answer

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

anonymous · Answer

is that the directrix

misty1212 · Answer

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

anonymous · Answer

okay

misty1212 · Answer

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

anonymous · Answer

so then it would just be 7/2

misty1212 · Answer

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

misty1212 · Answer

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

misty1212 · Answer

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