Question

Equation of tangent to curve x = a cos³t, y = a sin³t at 't' is –

• A. x sect – y cosec t = a
• B. x sec t + y cosec t = a
• C. x cosec t + y cosec t = a
• D. None of these

Answer 1

Answer: (B)

x sec t + y cosec t = a

Answer 2

$\frac{dx}{dt}$= – 3 a cos2t sin t $\frac{dy}{dt}$= 3a sin2t cost

$\frac{dy}{dx}$ = – tan t Ž y – a sin³t = – tan t (x– acos³t)

Ž y cost + x sin t – a sin³ t cos t–a sin t –cos³ t= 0

Ž x tan t + y cos t – a t sin t cos t = 0

Ž x sec t + y cosec t = a