What is the equation of a directrix of the parabola of x^2+ 4 x + 4 y - 4 = 2-0

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01-04-2018
Mathematics

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What is the equation of a directrix of the parabola of x^2+ 4 x + 4 y - 4 = 2-0

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sqdancefan sqdancefan · Answer 1 · 2018-04-01T20:48:57+02:00

You can rewrite the equation into the form
.. y = 1/(4p)*(x -h)^2 +k
In this form, (h, k) is the vertex and p is the distance from the focus to the vertex, or the vertex to the directrix.

.. x^2 +4x -6 = -4y . . . . . . . . . . . add -2-4y
.. (x +2)^2 -10 = -4y . . . . . . . . . . complete the square
.. (-1/4)*(x +2)^2 +2.5 = y . . . . . . the desired form

Then the distance from vertex (-2, 2.5) to the directrix is -1, which means the directrix is 1 unit above the vertex.

The equation of the directrix is y = 3.5.