Question

If equation of parabola whose vertex is at (5,4) and directrix is 3x + y - 29 = 0 is x² + ay² + bxy + cx + dy + k = 0 then a+b+c+d+k is

(a) 576

(b) 575

(c) -575

(d) -576

Answer 1

Correct option is (d) -576

Given, 

vertex (5, 4) & directrix at 3x + y - 29 = 0

Thus, foot of perpendicular from vertex to directrix

Thus, by calculating, focus will be (2, 3). 

Now, equation of parabola