SOLUTION: What type of directrix does this conic have? r = 4/-2-cosθ or https://s10.postimg.org/kbq3bkdpl/r_-2_-cos.png A.) Vertical B.) Horizontal C.) Oblique D.) No directrix.

Algebra ->  Test -> SOLUTION: What type of directrix does this conic have? r = 4/-2-cosθ or https://s10.postimg.org/kbq3bkdpl/r_-2_-cos.png A.) Vertical B.) Horizontal C.) Oblique D.) No directrix.      Log On


   

Question 1080588: What type of directrix does this conic have? r = 4/-2-cosθ or https://s10.postimg.org/kbq3bkdpl/r_-2_-cos.png
A.) Vertical
B.) Horizontal
C.) Oblique
D.) No directrix.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
r+=+4%2F%28-2-cos%28theta%29%29
r+=+4%2F-2%281%2B%281%2F2%29cos%28theta%29%29
r+=+-2%2F%281%2B%281%2F2%29cos%28theta%29%29.....compare to r+=+ed%2F%281%2B%28e%29cos%28theta%29%29 and you see that:
ed+=+-2 and e+=+1%2F2 and
%28-1%2F2%29d+=+2
d+=+-2%2F%281%2F2%29
d+=+-4
Since e+%3C+1, we have the equation of an ellipse. The form of the equation tells us that the directrix is perpendicular to the polar axis and that its Cartesian equation is x+=+-4 which is vertical line.
so, answer is: A.) Vertical

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
Dear tutor MathLover1 !


Do you agree that the radius "r" in polar coordinates is always positive and can not be negative ?


If you do agree, then how the formula r = 4%2F%28-2-cos%28theta%29%29 can produce the positive r ?