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

The Correct Option is C

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.