If the equation of the parabola, whose vertex is at $( 5,4 )$ and the directrix is $3 x + y - 29 = 0$, is $x ^ { 2 } + a y ^ { 2 } + b x y + c x + d y + k = 0$, then $a + b + c + d + k$ is equal to (1) 575 (2) - 575 (3) 576 (4) - 576
If the equation of the parabola, whose vertex is at $( 5,4 )$ and the directrix is $3 x + y - 29 = 0$, is $x ^ { 2 } + a y ^ { 2 } + b x y + c x + d y + k = 0$, then $a + b + c + d + k$ is equal to\\
(1) 575\\
(2) - 575\\
(3) 576\\
(4) - 576