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

JEE MATHEMATICS MCQ: PARABOLA

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Application +4 | -1

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is

3x + y - 29 = 0,

{x^2} + a{y^2} + bxy + cx + dy + k = 0,

then

a + b + c + d + k

is equal to

View answer and explanation

Correct option: D

–576

Option D (–576) is correct because after finding the focus and using the definition of a parabola, the coefficients of the resulting equation sum to -576.

More Questions from PARABOLA

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The equation of a common tangent to the parabolas

y=x^2

and

y=-(x-2)^2

is A point

P

moves such that slope of one tangent drawn from it to parabola

y^2=16 x

is four times the slope of other tangent, then the length of latus rectum of the conic represented by locus of

P

, is Let

P,Q,R

be three points on parabola

{y^2} = 4x

and normal at

P

and

R

meet at

Q

, then the locus of the mid-point of the chord

PR

is a parabola whose vertex is at The tangents at the end points of any chord through

(1,0)

to the parabola

y^2+4 x=8

intersect The focus of the parabola

x^2=-16 y

is If

I

denotes the semi-latusrectum of the parabola

{y^2} = 4ax

and

SP

and

SQ

denote the segments of any focal chord

PQ,S

being the focus, then

SP,l

and

SQ

are in the relation