Question

HELLPPP! @misty1212
y^2 + 6y - 2x + 13 = 0

Focus:

Directrix:

Length of focal chord:

Answer 1

\[y^2 + 6y - 2x + 13 = 0 \]

Answer 2

That's right

Answer 3

you know what this looks like?

Answer 4

you are going to have to do some work to find the vertex, which you need to start the problem
first you have to complete the square on the y term

Answer 5

I found the vertex already, (2, -3)

Answer 6

oh then you are9/10th of the way done
how did you find it?

Answer 7

A graphing calculator

Answer 8

oh

Answer 9

that does not help much

Answer 10

Why do you need to know HOW I found the vertex?

Answer 11

\[y^2+6y=2x-13\\
(y+3)^2=2x-13+9\\
(y+3)^2=2x-4\\
(y+3)^2=2(x-2)\] vertex is \((2,-3)\)

Answer 12

because if you find the vertex by making it look like
\[(y+3)^2=2(x-2)\] then finding the rest is easy

Answer 13

this looks just like
\[(y-k)^2=4p(x-h)\] a parabola that opens to the right with vertex \((h,k)\) and what you need is \(p\)
in your case \(4p=2\) and so \(p=\frac{1}{2}\)
your focus is \(\frac{1}{2}\) to the right of the vertex, the directrix is \(\frac{1}{2}\) units to the left

Answer 14

What the focal chord?

Answer 15

what is a focal cord?

Answer 16

no, what was the focal chord?

Answer 17

it does not ask for the focal chord, look carefully at the question dear

Answer 18

there is no one "focal chord" there are infinitely many
it asks for the LENGTH of the focal chord
that is \(4p\) which in your case is \(2\)

Answer 19

Ohhhhh, okay. Thanks