Question 1080597
general formula: {{{r =ed/(1-e*sin(theta))}}} where {{{e}}} is the eccentricity, directrix is {{{d}}} 

{{{r= 4/(-2-6sin(theta) )}}}......simplify first


{{{r= 4/-2(1+3sin(theta) )}}}


{{{r= -cross(4)2/cross(2)(1+3sin(theta) )}}}


{{{r= -2/(1+3sin(theta) )}}}

=>{{{ e=3}}}

{{{e> 1}}} , so the conic is a hyperbola

answer is: C.) {{{3}}}