Find the Equation of the Curve on Which the Point $P$

Multiple Choice

Find the equation of the curve on which the point $P$ lies. The distance between point $P$ and the point $( 0$ , 7) is $\frac { 7 } { 4 }$ of the distance between point $P$ and the line $y = - 4$ .

A) $\quad 616 x ^ { 2 } - 33 y ^ { 2 } - 16 y = 0$
B) $\quad 16 x ^ { 2 } - 33 y ^ { 2 } - 616 y = 59$
C) $\quad 16 x ^ { 2 } - 33 y ^ { 2 } - 616 y = 0$
D) $\quad 16 x ^ { 2 } - 33 y ^ { 2 } + 616 y = 0$
E) none of these