Question

What is an equation of a parabola with the given vertex and focus?

vertex: (–2, 5); focus: (–2, 6)

Answer 1

the parabola is concave in the direction from V(-2,5) to F(-2,6). In this problem, it opens to the right. so the correct equation is \[\large (y-k)^2=4p(x-h)\] where the vertex has coordinates \[\large V(h,k)\] and \(\large p\) is the directed distance from the vertex to the focus.

Answer 2

oops, the parabola opens upward, so the correct equation is \[\large 4p(y-k)=(x-h)^2\]

Answer 3

so where do i plug in the points i dont see a f or v in this

Answer 4

the focus is F, the vertex is V

Answer 5

oh okay so where do i plug in points

Answer 6

in the equation \[\large 4p(y-k)=(x-h)^2\]
\[\large V(h,k) = V(-2,5)\]

Answer 7

so then it's 4p(y-5)=(x-2)^2?

Answer 8

it would be \[\large 4p(y-5)=(x+2)^2\]
compute p as the directed distance from V to F, using the distance formula.

Answer 9

did you give me the distance formula already? cause i dont know what it is

Answer 10

the distance formula: \[\large \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]

Answer 11

wait im kind of confused i dont know how to do this formula