# Homework Help: Family of curves problem

1. Dec 13, 2009

### aspirare21

1. The problem statement, all variables and given/known data
Parabolas with vertex on the x-axis,with axis parallel to the y-axis,and with distance from focus to vertex fixed as "a".

the question is pick your own value of "a". Then for "a" value pick value of "h". What does it mean? I'm confuse.. T__T

2. Relevant equations
(x-h)² = ±4a(y-k)
(x-h)² = ±4ay

k=0

3. The attempt at a solution

(x-h)² =4ay
2(x-h) =4ay'

square both sides
(x-h)² = 4a²(y')²

substitute
4a²(y')² = 4ay
a(y')² = y

I don't know what will happen if i choose a value of "a" then it will generate a value of "h".. T__T

2. Dec 13, 2009

### ideasrule

Is that all the question says? Is there another part to the question? If not, OK, a=2 and h=3. Any value of a and h except a=0 will satisfy the conditions given in the question.

3. Dec 13, 2009

### aspirare21

I forgot.. the answer should be in differential equation. show that when you pick "a" you should derive "h". Kindly confusing to me..