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
