Question

Can you please help me with this problem. :)

Find the coordinates of the vertex, focus, ends of the lactus rectum and the equation of the directrix.
>>y^2 = -11x
>>x^2= -6y

Answer 1

thank you @aric200 :)

Answer 2

this is two problems right?

Answer 3

yes @satellite3 .. can you pls help me :)

Answer 4

sure
first of all lets do \[y^2 = -11x\]

Answer 5

*73 sorry

Answer 6

lol np

Answer 7

do you know what
\[y^2 = -11x\] looks like? we need that to start then it is easy

Answer 8

uhmm its a parabola that faces on the negative axis of x?

Answer 9

yes

Answer 10

there is my crappy picture but you get the idea

Answer 11

general form is
\[(y-k)^2=4p(x-h)\] where the vertex is \((h,k)\)
you have
\[y^2=-11x\] making \((h,k)=(0,0)\) in other words the vertex is at the origin
ok so far?

Answer 12

i think Ive quite got it. :)

Answer 13

ok now we need the focus and directrix right?

Answer 14

yes. :D hehe im quite confused on how to solve it.

Answer 15

ok lets look at the general form
\[(y-k)^2=4p(x-h)\] and the specific one you have
\[y^2=-11x\]

Answer 16

we already used that to find the vertex is \((0,0)\) now we need to find the directrix
from
\[y^2=-11x\] we see that \(4p=-11\)
solveing for \(p\) means
\[p=-\frac{11}{4}\]

Answer 17

that means the focus is \(\frac{11}{4}\) units to the LEFT of the vertex, namely at
\[(-\frac{11}{4},0)\]

Answer 18

and the directrix is \(\frac{11}{4}\) units to the RIGHT

Answer 19

namely at \(x=\frac{11}{4}\)

Answer 20

that is why you need to know what it looks like before you start
to know what direction to go in to find the focus and the directrix

Answer 21

ohh.. i think ive got it!. and is the directrix the line that passes through the x axis?

Answer 22

yes like this