what is the length of the focal chord?
y²+6y-2x+13=0

Question

what is the length of the focal chord?
y²+6y-2x+13=0

anonymous · Answer

no idea for this one 
but i bet we could look it up

anonymous · Answer

i've searched everywhere for these and can't seem to find them on the graphing websites, do you know a good one?

anonymous · Answer

https://www.wolframalpha.com/input/?i=parabola+y^2%2B6y-2x%2B13%3D0

anonymous · Answer

if you type in "parabola" it will give you the focus etc

anonymous · Answer

THANKS!!! so its 1 then? is the focal parameter the same as the length of the focal chord?

anonymous · Answer

no i think the length of the focal chord is the coefficient of the $x$ term

anonymous · Answer

what would that be?

anonymous · Answer

$$y ^{2}+6y-2x+13=0$$$$y ^{2}+6y=2x-13$$complete the square
$$y ^{2}+6y+9=2x-13+9$$$$(y+3)^{2}=2x-4$$standard form of a parabola$$(y+3)^{2}=2(x-2)$$vertex:(2,-3)
4p=2
4p is the length of the latus rectum... a focal chord parallel to the directrix.

anonymous · Answer

There are many focal chords though... I'm not sure which one your problem refers to... the most famous is the latus rectum... but a focal chord is a line segment that connects opposite sides of a parabola while passing through the focus.

anonymous · Answer

probably the most common one, what would that be?

anonymous · Answer

4p=2... the latus rectum is 2 units long for this parabola.

anonymous · Answer

It is the coefficient of the non-squared term in the equation above.

anonymous · Answer

so is 4p=2 the final answer?

anonymous · Answer

probably just 2

anonymous · Answer

thank you so much :) could one of you help me with another problem?

anonymous · Answer

post it new

anonymous · Answer

i will