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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Ellipse

NTA Abhyas 2020 · Mathematics · Ellipse

The length of the latus rectum of the curve represented by x = 3...

The length of the latus rectum of the curve represented by

x = 3

\left(cos t + sin t\right)

and

y = 4\left(cos t - sin t\right), is

Options

A $\dfrac{9}{2}$ units
B $9\sqrt{2}$ units
C $\dfrac{32\sqrt{2}}{3}$ units
D $\dfrac{9}{\sqrt{2}}$ units

Correct answer

D. $\dfrac{9}{\sqrt{2}}$ units

Step-by-step solution

\dfrac{x}{3} = cos t + sin t

and

\dfrac{y}{4} = cos t - sin t

{\left(\dfrac{x}{3}\right)}^{2} + {\left(\dfrac{y}{4}\right)}^{2} = 2

\dfrac{x^{2}}{{\left(3\sqrt{2}\right)}^{2}} + \dfrac{y}{{\left(4\sqrt{2}\right)}^{2}} = 1

Hence, the length of the latus rectum

= \dfrac{2{\left(3\sqrt{2}\right)}^{2}}{4\sqrt{2}} = \dfrac{9}{\sqrt{2}}

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