If the focus of a parabola divides a focal ch | vedclass

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

Question

(D) Let the lengths of the segments of the focal chord be $l_1 = 5$ and $l_2 = 3$.For a parabola,the semi-latus rectum $L$ is the harmonic mean of the

Vedclass · Accepted Answer

$\frac{15}{2}$

Vedclass · Answer

(D) Let the lengths of the segments of the focal chord be $l_1 = 5$ and $l_2 = 3$.For a parabola,the semi-latus rectum $L$ is the harmonic mean of the segments of any focal chord.Thus,$L = \frac{2 l_1 l_2}{l_1 + l_2}$.Substituting the values,$L = \frac{2 	imes 5 	imes 3}{5 + 3} = \frac{30}{8} = \frac{15}{4}$.The length of the latus rectum is $2L$.Therefore,the length of the latus rectum $= 2 	imes \frac{15}{4} = \frac{15}{2}$ units.

If the focus of a parabola divides a focal chord of the parabola into segments of lengths $5$ and $3$ units,then the length of the latus rectum of that parabola is:

Similar Questions

If $(x_1, y_1)$ and $(x_2, y_2)$ are the points on the parabola $y^2 = 32x$ each at a focal distance of $10$ units,then $2(x_1^2 + x_2^2 + y_1^2 + y_2^2) = $

The equation of the latus rectum of a parabola is $x + y = 8$ and the equation of the tangent at the vertex is $x + y = 12$. The length of the latus rectum is:

The condition for the line $y=mx+c$ to be a normal to the parabola $y^{2}=4ax$ is

Find the length of the latus rectum of a parabola if $PSQ$ is a focal chord such that $SP = 3$ and $SQ = 2$.

How many parabolas can be drawn if the two endpoints of the latus rectum are given?

Vedclass Test Series

Exam Paper Generator

Online Exam Module