Hyperboloid of One Sheet

eq1: (-(x^(2) / 25)) + y^(2) / 4 + z^(2) / 100 = 1
k = -31 (slider from -50 to 50, step 1)
p: x = k
m = 11 (slider from -30 to 30, step 1)
q: y = m
n = 50 (slider from -80 to 80, step 5)
r: z = n
c = IntersectPath(p, eq1)
d = IntersectPath(q, eq1)
e = IntersectPath(r, eq1)