Question

Find an equation for the parabola with focus at (10, -4) and vertex at (3,-4)

Answer = y^2 + 8y - 28x + 100 = 0

Answer 1

the distance between the vertex and the focus is the quantity a in
4a(y-k)=(x-h)^2
where (h,k) is the vertex.
h=3
k=-4
so just find the distance between the vertex and focus. and plug in all those values.

Answer 2

ooh..
after that put in general form.. :)

Answer 3

the line of symmetry is y = -4
so the parabola is concave right and has

the general form is \[4a(x -h) = (y - k)^2 \]


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

which gives a = 7 and since the focus is above the verex the parabola is concave up

\[4 \times 7(x -3) = (y + 4)^2\]

expand and simplify will give your answer

Answer 4

And there are 3 other forms, correct?