coordinate geometry about parabolas

**fishlord40** · February 2nd 2010, 02:46 AM

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!!

**earboth** · February 2nd 2010, 03:51 AM

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

$4py = x^2$

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

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

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

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

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