The equation of tangent to the curve $x= a cos^3t, y =a\, sin^3t$ at t is :
Answer & explanation
Correct answer: option 1
The correct answer is option (1) → $x\sec t+y\,cosec\,t=a$
$x= a \cos^3t, y =a\sin^3t$
$\frac{dx}{dt}=-3\cos^2y\sin t$, $\frac{dy}{dt}=3a\sin^2t\cos t$
so $\frac{dy}{dx}=\frac{-\sin t}{\cos t}$
so eq. → $y-a\sin^3t=\frac{-\sin t}{\cos t}(x-a\cos^3t)$
$y\,cosec\,t-a\sin^2t=a\cos^2t-x\sec t$
$x\sec t+y\,cosec\,t=a$