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ribbons1202bows · Jul 1, 2009, 01:47 PM

I am working with parabolas and I completely don't understand it. I need to fine the vertex and focus, the axis of symmetry and directrix and the direction of opening of the parabola. I also have to find the length of the latus rectum. I just need a sense of direction to be able to get started and some instruction on the terms and equations of how to get started working this problem. I was looking at form of equation for parabolas and I don't know whether to use y=a(x-h)^2+k or x=a(y-k)^2 + h or if I even need to use either one. Please help me to understand.

Perito · Jul 1, 2009, 02:57 PM

Wikipedia has a great discussion on the parabola:

Parabola - Wikipedia, the free encyclopedia

Basically, parabolas can have one of two forms, as you noted. You need to take the equation you have (I presume you have an equation) and put it into one of those forms. It will only go into one of them -- not both.

$(x-h)^2 = 4p(y-k) \,\,\,or \,\,\, (y-k)^2=4p(x-h)^2$

The first has the axis parallel to the y axis. The vertex is (h,k). The focus is (h,k + p), and the directrix is the line, y = k − p. P is the distance from the vertex to the focus.

The second has the axis parallel to the x-axis.