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 ,
13) is $\frac { 13 } { 7 }$ of the distance between point $P$ and the line $y = - 7$ .

A) $\quad 49 x ^ { 2 } - 120 y ^ { 2 } + 3,640 y = 0$
B) $\quad 49 x ^ { 2 } - 120 y ^ { 2 } - 3,640 y = 0$
C) $\quad 49 x ^ { 2 } - 120 y ^ { 2 } - 3,640 y = 69$
D) $\quad 3,640 x ^ { 2 } - 120 y ^ { 2 } - 49 y = 0$
E) none of these