1. coordinate geometry about parabolas

A chord of the parabola that is perpendicular to the axis and 1 unit from the vertex has a length of 1 unit. How far is the vertex from the focus?

***by the way, the answer to this problem is 1/16. I just want to know how did you get the right answer to this problem. thanks!!

2. Originally Posted by fishlord40
A chord of the parabola that is perpendicular to the axis and 1 unit from the vertex has a length of 1 unit. How far is the vertex from the focus?

***by the way, the answer to this problem is 1/16. I just want to know how did you get the right answer to this problem. thanks!!
1. Let the equation of the parabola be

$\displaystyle 4py = x^2$

where p is the distance of the focus from the vertex.

2. You know the coordinates of 2 points of the parabola: $\displaystyle P(-\tfrac12, 1)$, $\displaystyle Q(\tfrac12, 1)$

3. Plug in the coordinates of Q into the equation of the parabola and solve for p:

$\displaystyle 4p \cdot 1 = \left(\frac12\right)^2$