Exam

NTA Abhyas

Year

2020

Subject

Mathematics

Chapter

Parabola

NTA Abhyas 2020 · Mathematics · Parabola

The length of the focal chord of the parabola y^ 2 = 4x at a...

The length of the focal chord of the parabola $y^{2} = 4x$ at a distance of $0.4$ units from the origin is

Step-by-step solution

Let,& $PQ$ is a focal chord and $S$ is the focus
Now, $OS = 1$
$⇒$ In $\Delta OSR$ ($R$ is the foot of the perpendicular from $O$ on $PQ$)
$⇒ cosec\theta = \dfrac{1}{0 . 4} = 2 . 5$
Length of $PQ$ is equal to the length of latus rectum$\times cosec^{2}\theta$
$⇒ PQ = 4\left(2.5\right)2 = 4 \times 6.25$
$= 25$