Question

Help me find these? Vertex, Focus, Directrix, and Length of focal chord. for y^2+6y-2x+13=0 Any help is appreciated!

Answer 1

complete the square in y after rewriting the equation as

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

Answer 2

this is a parabola which is concave right...


the general form is

\[(y - k)^2 = 4a(x - h)\]

the vertex is (h, k) a = focal length

Answer 3

so vertex would be -13,6 and focal length is 2? @campbell_st

Answer 4

Ummm no

its

\[(y + 3)^2 = 2(x - 2)\]

so it looks like the focal length is 1/2 and the vertex is (2, -3)

Answer 5

your parabola looks like