PQ is any focal chord of the parabola y^2=32x | vedclass

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

Question

(C) The given equation of the parabola is $y^2=32x$.Comparing this with the standard form $y^2=4ax$,we get $4a=32$,which implies $a=8$.The length of a

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(C) The given equation of the parabola is $y^2=32x$.Comparing this with the standard form $y^2=4ax$,we get $4a=32$,which implies $a=8$.The length of a focal chord of a parabola $y^2=4ax$ is given by $L = a(t + \frac{1}{t})^2$,where $t$ is the parameter of one end of the chord.The minimum length of a focal chord is the length of the latus rectum,which is $4a$.Therefore,the minimum length $= 4 	imes 8 = 32 	ext{ units}$.Thus,the length of $PQ$ can never be less than $32$ units.

$PQ$ is any focal chord of the parabola $y^2=32x$. The length of $PQ$ can never be less than: ............ $unit$

Similar Questions

If the line $lx + my + n = 0$ is a tangent to the parabola $y^2 = 4ax$,then the locus of its point of contact is

If the tangent at a point $P$ on a parabola makes an angle $\alpha$ with its focal distance,then the angle between the tangent and the axis of the parabola is:

The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is

The shortest distance from $(0,3)$ to the parabola $y^2=4x$ is

If a parabolic reflector is $20 \, cm$ in diameter and $5 \, cm$ deep,find the focus.

Vedclass Test Series

Exam Paper Generator

Online Exam Module