If the equation of the parabola, whose vertex is at (5,4) and the directrix is 3 x+y-29=0, is x2+a y2+b x y+c x+d y+k=0 then a+b+c+d+k is equal to

Question

If the equation of the parabola, whose vertex is at (5,4) and the directrix is 3 x+y-29=0, is x2+a y2+b x y+c x+d y+k=0 then a+b+c+d+k is equal to (A) 575 (B) -575 (C) 576 (D) -576

Tardigrade Admin · Accepted Answer

Vertex (5,4) Directrix: 3 x+y-29=0 Co-ordinates of B (foot of directrix) (x-5/3)=(y-4/1)=-((15+4-29/10))=1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3aca69885da679d8ae03a89b2709e865-.png" /> x=8, y=5 S=(2,3) (focus) Equation of parabola P S=P M so equation is x2+9 y2-6 x y+134 x-2 y-711=0 a+b+c+d+k=9-6+134-2-711=-576

Q. 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+b+c+d+k is equal to

575

-575

576

-576

Vertex (5,4) Directrix : 3x+y−29=0 Co-ordinates of B (foot of directrix) 3x−5​=1y−4​=−(1015+4−29​)=1 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

Q. 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