FE Exam Review - Analytic Geometry - Parabola

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[@sekhar4876]

Thanks for the Clear explanation of concepts!

[@tonynwaiwu761]

What happened to the negative sign attached to the formula for the directrix x=-p/2?

[@scorpionyrsd2469]

The standard from of the parabola is (x - h) ^2 = 4 p ( y - k) and p is the distance from the vertex to the directrix or form the vertex to the focus. It means that if the distance from the vertex to the directrix is 3 units , then you substitute 3 in the equation 4 p ( 4X3)= 12. Also, having the vertex point ( 4,8), the right answer is B. Thanks

[@jcd6759]

Hey, The standard form for the parabola is actually (x - h) ^2 = 2 p ( y - k) using the ncees manual. My understanding is that the distance from the Directrix to the Focus is P, therefore the distance from vertex to directrix is P/2. Considering that this parabola opens upward we have the vertex point ,(h,k), of (4,8) in this case. and the directrix at y=5, we are able to calculate what P is, P/2= 8-5 which then leads to P=2(8-5)= 6. Plug that 6 and the (4,8) into the standard form equation we then get (X-4) ^2 = 2 (6) ( y - 8). We are able to confirm that the answer is B .Lets discuss if you see fit.

[@cobygualano3881]

How does the negative for the directrix cancel out?

[@directhubfeexam]

Hi Coby, the FE Handbook shows the specific case where the directrix, x = constant, that's a vertical line for a parabola.
Per FE Handbook, The negative directrix, x = -p/2 or x = Vertex (x coordinate) - p/2 ---> x = 0 - p/2. This will be a vertical line that lies to the left of 0 on the x-axis.
For this problem, the directrix will be, y = Vertex (y coordinate) - p/2 ---> y = 8 - 6/2 = 5

[@cobygualano3881]

​@@directhubfeexam okay got it! Thanks for the fast reply!