If x = a cos^3 theta and y = b sin^3 theta,th | vedclass

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

Question

(C) Given $x = a \cos^3 	heta$ and $y = b \sin^3 	heta$. Dividing by $a$ and $b$ respectively,we get $\frac{x}{a} = \cos^3 	heta$ and $\frac{y}{b}

Vedclass · Accepted Answer

$(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = 1$

Vedclass · Answer

(C) Given $x = a \cos^3 	heta$ and $y = b \sin^3 	heta$. Dividing by $a$ and $b$ respectively,we get $\frac{x}{a} = \cos^3 	heta$ and $\frac{y}{b} = \sin^3 	heta$. Taking the power of $1/3$ on both sides,we get $(\frac{x}{a})^{1/3} = \cos 	heta$ and $(\frac{y}{b})^{1/3} = \sin 	heta$. Squaring both sides,we get $(\frac{x}{a})^{2/3} = \cos^2 	heta$ and $(\frac{y}{b})^{2/3} = \sin^2 	heta$. Adding these two equations,we get $(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = \cos^2 	heta + \sin^2 	heta$. Since $\cos^2 	heta + \sin^2 	heta = 1$,we have $(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = 1$.

If $x = a \cos^3 \theta$ and $y = b \sin^3 \theta$,then:

Similar Questions

In a $\Delta ABC$,if the median,bisector,and altitude drawn from the vertex $A$ divide the angle at the vertex into four equal parts,then the angles of the $\Delta ABC$ are:

If $\theta \in \left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$, then the value of $\sqrt{4 \cos^{4} \theta + \sin^{2} 2 \theta} + 4 \cot \theta \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

If $r \sin \theta = 3$ and $r = 4(1 + \sin \theta)$ for $0 \le \theta \le 2\pi$,then $\theta = $

If $\operatorname{Sinh}^{-1} x = \operatorname{Cosh}^{-1} y = \log(1+\sqrt{2})$, then $\operatorname{Tan}^{-1}(x+y) = $

$\cos \frac{7 \pi}{8}+\cos \frac{\pi}{4}+\cos \left(\frac{-\pi}{8}\right)-1=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module