If PSQ is a focal chord of the parabola y^2 = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a parabola $y^2 = 4ax$,the semi-latus rectum is the harmonic mean of the segments of any focal chord.Given $y^2 = 8x$,we have $4a = 8$,so $a =

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) For a parabola $y^2 = 4ax$,the semi-latus rectum is the harmonic mean of the segments of any focal chord.Given $y^2 = 8x$,we have $4a = 8$,so $a = 2$.The semi-latus rectum $l = 2a = 4$.Let the segments of the focal chord be $SP$ and $SQ$. Then $SP, l, SQ$ are in harmonic progression.Therefore,$l = \frac{2(SP)(SQ)}{SP + SQ}$.Substituting the values $l = 4$ and $SP = 6$:$4 = \frac{2(6)(SQ)}{6 + SQ}$$4 = \frac{12(SQ)}{6 + SQ}$$4(6 + SQ) = 12(SQ)$$24 + 4(SQ) = 12(SQ)$$24 = 8(SQ)$$SQ = 3$.

If $PSQ$ is a focal chord of the parabola $y^2 = 8x$ such that $SP = 6$,then find the length of $SQ$.

Similar Questions

Find the equation of the normal to the parabola $y^2 = 16x$ having a slope of $-1/4$.

Let $P(4, -4)$ and $Q(9, 6)$ be two points on the parabola $y^2 = 4x$. Let $X$ be any point on the arc $POQ$ of this parabola,where $O$ is the vertex,such that the area of $\Delta PXQ$ is maximum. Then this maximum area (in sq. units) is

If the lines $y = x$ and $y = -x$ intersect the parabola $y^2 = 4x$ at points $A$ and $B$ respectively,other than the origin,what is the length of $AB$?

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $y^{2}=12x$.

If the line $y = 2x + k$ is a tangent to the curve $x^2 = 4y$,then $k$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module