CUET · MATHS · PYQ PAPER 2023
The equation of tangent to the curve given by \(x=a \sin ^3 t, y=b \cos ^3 t\) at a point where \(t=\frac{\pi}{2}\) is :
- A \(x=0\)
- B \(y=0\)
- C \(y=\frac{\pi}{2}\)
- D \(x=\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(B) \(y=0\)
Step-by-step Solution
Detailed explanation
\(x_1 = a \sin^3(\frac{\pi}{2}) = a(1)^3 = a\) \(y_1 = b \cos^3(\frac{\pi}{2}) = b(0)^3 = 0\) \(\frac{dx}{dt} = 3a \sin^2 t \cos t\) \(\frac{dy}{dt} = -3b \cos^2 t \sin t\)…
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