How do you write the equation of the directrix of the conic section: -y^2 -4x +4y -4=0?

L

Lina

New member
Write the equation of the directrix of the conic section shown below.

Write your answer without using spaces.
-y^2 -4x +4y -4=0
 
-y^2 - 4x + 4y - 4 = 0
==> y^2 + 4x - 4y + 4 = 0

This appears to be a parabola with a vertical directix.

y^2 + 4x - 4y + 4 = 0
==> y^2 - 4y + 4 = -4x
==> (y - 2)^2 = -4x
==> (-1/4)(y - 2)^2 + 0 = x

Comparing the leading coefficent in-front of the squared binomial, we see that p = -1. The directix is given by y = k - p. In this case, h = 2.

x = h - p
==> x = 2 - (-1)
==> x = 3

Therefore, the equation of the directix is x = 3.

Hope this helps!
 
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