If b and c are the lengths of the segments of | vedclass

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

Question

(C) Let the focal chord of the parabola $y^2 = 4ax$ be divided into two segments of lengths $b$ and $c$ by the focus $(a, 0)$.If the semi-latus rectum

Vedclass · Accepted Answer

$\frac{2bc}{b + c}$

Vedclass · Answer

(C) Let the focal chord of the parabola $y^2 = 4ax$ be divided into two segments of lengths $b$ and $c$ by the focus $(a, 0)$.If the semi-latus rectum of the parabola is $l$,then the lengths of the segments of a focal chord are related to the semi-latus rectum by the harmonic mean property.Specifically,the semi-latus rectum $l$ is the harmonic mean of the segments $b$ and $c$.Therefore,$\frac{1}{l} = \frac{1}{2} (\frac{1}{b} + \frac{1}{c})$.$\frac{1}{l} = \frac{1}{2} (\frac{b + c}{bc})$.Thus,$l = \frac{2bc}{b + c}$.

If $b$ and $c$ are the lengths of the segments of any focal chord of the parabola $y^2 = 4ax$,then what is the length of the semi-latus rectum?

Similar Questions

The number of points on the parabola $y^2=x$ at which the slope of the normal drawn at the point is equal to the $x$-coordinate of that point is

The position of a moving point in the $XY$-plane at time $t$ is given by $\left( (u \cos \alpha)t, (u \sin \alpha)t - \frac{1}{2}gt^2 \right)$,where $u, \alpha, g$ are constants. The locus of the moving point is

The locus of the midpoint of the focal radii of a variable point moving on the parabola $y^2 = 4ax$ is a parabola whose:

The length of the normal chord to the parabola $y^2 = 4x$,which subtends a right angle at the vertex,is

The equation of the tangent to the parabola $y^2=12x$,which makes an angle $30^{\circ}$ with the positive direction of the $X$-axis is given by $x-\sqrt{3}y+9=0$. The point of contact is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module