Question

Write the equation of a parabola with a vertex at (5, 2) and a directrix y = 1

Answer 1

If the directrix is y = 1 and the vertex is at (5,2), where is the focus?

Answer 2

there wasn't a focus .--.

Answer 3

No, you have to figure it out!

Answer 4

can you should how to find the focus? I know it's something like from the orgin?

Answer 5

But it isn't difficult — the focus and the vertex and the directrix are equal distances apart

Answer 6

You know that the focus and vertex are on a line which is perpendicular to the directrix

the distance between directrix and vertex is the same as the distance between vertex and focus.

Answer 7

so 5?

Answer 8

the latter is because the parabola is the set of all points equidistant from the focus and directrix. the vertex is the point where the distance is shortest to both focus and directrix.

Answer 9

well, the focus is a point, and you just gave me a single number. that doesn't specify a point on a plane...

Answer 10

there is a 5 in the answer, however, so you're getting warm :-)

Answer 11

oh my gosh I'm so confused. okay can we start from the beginning? lol.

Answer 12

why don't you tell me what the beginning is?

Answer 13

do you understand the definition of a parabola, and what the directrix, vertex, and focus mean?

Answer 14

okay what is the equation? isn't like v(x)= a (x-h)^2 +k ?

Answer 15

equation might be a bit premature if you don't have a good handle on what a parabola is...

Answer 16

okay can we go over what the diretrex is?

Answer 17

I'm super lost in all of this.

Answer 18

The directrix is a line.