Question

Find the equation of the parabola with focus (5, 0) and directrix x = -5.

Answer 1

@satellite73

Answer 2

again we need a picture
this one will open to the right, so that the \(y\) term will be squared

Answer 3

ok. how do we know it will be opened to the right ?

Answer 4

because \(x=-5\) is a VERTICAL line and \((5,0)\) is to the right of it

Answer 5

oh ok . whats next ?

Answer 6

we know the vertex is half way between \((5,0)\) and \(x=-5\) namely at \((0,0)\)

Answer 7

and we know the distance between the vertex and the focus is \(5\)
all these should be clear without using any formulas
if they are not, let me know

Answer 8

then since the \(y\) term is squared and the vertex is \((0,0)\) your equation is
\[4p(x-h)=(y-k)^2\] or
\[4\times 5(x-0)=(y-0)^2\] or just
\[20x=y^2\]

Answer 9

ok . thats fairly easy to understand .