how to find the vertex, focus , latus rectum and the directrice if the equation is x^2-4x-12y-20=0

Here's your answer, I hope you learn from it and apply this knowledge towards other questions.

x^2-4x-12y-20=0 - Wolfram|Alpha (http://www.wolframalpha.com/input/?i=x%5E2-4x-12y-20%3D0&t=crmtb01)

wana: you need to cmvret the equation into the standard for, which is:


(x-x_1)^2 = 4p (y-y_1)


where x_1, \ y_1, \ p are constants. You should be able to get the equation into this form through algebra manipulation. Once you have this then the vertex is at (x_1,y_1) and the focus is p units away from the vertex towards the inside of the parabola. The latus rectum is the line that passes through the focus that is perpendicular to the axis of symmetry. The directriox is a line also perpendicular to the axis of symmetry but passing through a point p units from the vertex on the outside of the parabola.

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