Question

The portion of the tangent to the curve x$^{\frac{2}{3}}$+y$^{\frac{2}{3}}$=a$^{\frac{2}{3}}$, a>0 at any point of it, intercepted between the axes

• A. varies at abscissa
• B. varies as ordinate
• C. is constant
• D. varies as the product of abscissa and ordinate

Answer 1

Answer: (C)

is constant

Answer 2

The correct answer is option (C) is constant

The parametric equations are x=a cos3θ, y=a sin2θ

$\frac{dx}{d\theta}=3a\,cos^2t(-sin\theta),\frac{dy}{d\theta}$

= $3a\,sin^2\theta cos\theta\frac{dy}{dx}=-tan\theta$

Equation of the tangent is $y-a\,sin^3\theta$

$\Rightarrow \frac{x}{a\,cos\theta}+\frac{y}{a\,sin\theta}=1$

If the tangent cuts the axes at A and B respectively,then A=($a\,cos\theta,0$) and B=($0,a\,sin\theta$)

It means constant.