If the 4th term in the expansion of $\left(p x+\frac{1}{x}\right)^n, n \in N$ is $\frac{5}{2}$ and three normals to the parabola $y^2=x$ are drawn through a point $(q, 0)$, then

JEE MATHEMATICS MCQ: PARABOLA

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If the 4th term in the expansion of

\left(p x+\frac{1}{x}\right)^n, n \in N

\frac{5}{2}

and three normals to the parabola

y^2=x

are drawn through a point

(q, 0)

, then

View answer and explanation

Correct option: B

q>p

Option B (

q>p

) is correct because the condition for three normals to a parabola to be drawn from a point (q,0) implies q > 2a, and we find p = 1/2 and a = 1/4, thus q > p.

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