Question

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

(A) 575 

(B) –575 

(C) 576 

(D) –576

Answer 1

Correct option is (D) –576

Vertex (5,4) 

Directrix : 3x + y – 29 = 0 

Co-ordinates of B (foot of directrix)

x = 8, y = 5 

S = (2, 3) (focus) 

Equation of parabola 

PS = PM 

so equation is

x² + 9y² – 6xy + 134x – 2y – 711 = 0 

a + b + c + d + k = 9 – 6 + 134 – 2 – 711 = – 576