Question

What is the equation of a parabola with vertex (0, 0) and a focus at (2, 0)

Answer 1

didn't we just do this?

Answer 2

nope, we did (0, 0) and (0, 2)

Answer 3

(0, 6)*

Answer 4

oh i see, this time the focus is on the \(x\) axis
looks like

Answer 5

i could've used the equation you gave me but didn't know if something different happened because the x and y's are switched

Answer 6

so this time instead of \(4py=x^2\) we have \(4px=y^2\)

Answer 7

yeah if it opens left or right, the \(y\) term is squared, not the \(x\) term

Answer 8

but now it is easy right? you have
\[4px=y^2\] and \[p=2\]

Answer 9

8x = y^2

Answer 10

what about something like the equation of a parabola with vertex (0, 0) and directrix x = -3