11. The equation of a parabola is given y=1/2x^2+6x+24.

What is the equation of the directrix of the parabola?

12. The equation of the parabola is (y-1)^2=16(x+3).

What is the equation of the directrix of the parabola?

Guest May 3, 2017

#1**+1 **

11. The equation of a parabola is given y=1/2x^2+6x+24.

What is the equation of the directrix of the parabola?

First.....find the vertex.....complete the square on x and y

y = (1/2) [ x^2 + 12 x + 36 + 24 - 36 ]

y = (1/2) [ (x + 6)^2 - 12 ]

y = (1/2) (x + 6)^2 - 6 the vertex is ( -6, - 6) ....add 6 to both sides

(y + 6) = (1/2) (x + 6)^2 multiply both sides by 2

2(y + 6) = ( x + 6)^2

And in the form 4p (y - k) = (x + 6)^2

4p = 2

p = 1/2

So......the equation of the directrix is y = -6.5

12. The equation of the parabola is (y-1)^2=16(x+3).

What is the equation of the directrix of the parabola?

The vertex is ( -3, 1) and the parabola opens to the right

The form is

(y - k)^2 = 4p(x + 3)

So 4p = 16 → p = 4

And the equation of the directrix is x = -7

CPhill
May 3, 2017