Question 1136327
given:

{{{e=5}}}=>{{{e>0}}}-> hyperbola
 and directrix {{{y = -6}}} =>horizontal main axis
{{{d }}} = distance between focus(pole) and directrix => distance from ({{{0}}},{{{0}}}) to ({{{0}}},{{{-6}}}) is {{{6}}}

or, directrix {{{y = -6}}}=>{{{y= -d}}}=>{{{d=6}}}

The sine function appears in the denominator, so the hyperbola is horizontal. 
so, you will use formula {{{ r =  ed/(1- e*sin(theta))}}}

 {{{r =  (6*5)/(1- 5*sin(theta))}}}
{{{r =  30/(1-5sin(theta))}}}


{{{ graph( 600, 600, -10, 10, -10, 10,-sqrt((x^2+37.5)/24)-6.25 , sqrt((x^2+37.5)/24)-6.25,-6) }}}