# Find the focus and directrix of the parabola

• Jun 8th 2010, 04:41 PM
htk
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!
• Jun 8th 2010, 11:15 PM
earboth
Quote:

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:

$(y-h)^2=4p(x-k)$ 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:

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

3. Determine V, F and d.
• Jun 9th 2010, 04:53 AM
htk
So, V (3,0) F=(25/8, 0) D x= 23/8 Are these correct? Thanks again!

4p= 1/2
p= 1/8
• Jun 9th 2010, 07:56 AM
earboth
Quote:

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! (Clapping)