Thread: Find the focus and directrix of the parabola

1. Find the focus and directrix of the parabola

Find the focus, directrix and axis of the parabola with equation x= 2y^2+3?
x-3= 2y^2

x-3 = y^2 -------------> Is it how you solve it?

Thank you for helping me!

2. Originally Posted by htk
Find the focus, directrix and axis of the parabola with equation x= 2y^2+3?
x-3= 2y^2

x-3 = y^2 -------------> Is it how you solve it?

Thank you for helping me!
1. This is a parabola opening to the right. The general equation of such a parabola is:

$\displaystyle (y-h)^2=4p(x-k)$ where V(k, h) is the vertex, F(k+p, h) is the focus and d: x = k-p is the equation of the directrix.

2. Transform the given equation into the general form:

$\displaystyle x= 2y^2+3~\implies~(y-0)^2=\frac12(x-3)~\implies~(y-0)^2=4 \cdot \frac18(x-3)$

3. Determine V, F and d.

3. So, V (3,0) F=(25/8, 0) D x= 23/8 Are these correct? Thanks again!

4p= 1/2
p= 1/8

4. Originally Posted by htk
So, V (3,0) F=(25/8, 0) D x= 23/8 Are these correct? Thanks again!

4p= 1/2
p= 1/8
Perfect!