TS EAMCET · Maths · Application of Derivatives
The equation of the normal at \(t=\frac{\pi}{2}\) to the curve \(\mathrm{x}=\) \(2 \sin t, y=2 \cos t\) is
- A \(x=2\)
- B \(y=0\)
- C \(y=2x+3\)
- D \(y=3\)
Answer & Solution
Correct Answer
(B) \(y=0\)
Step-by-step Solution
Detailed explanation
\(x=2 \sin t, y=2 \cos t\) \(\therefore \quad x^2+y^2=4\) Differentiating both sides wrt \(x\), \(2 x+2 y \frac{d y}{d x}=0 \Rightarrow \frac{d y}{d x}=\frac{-x}{y}\) \(\therefore \quad\) Slope of normal \(=\frac{y}{x}\) \(\therefore \quad\) Equation of normal at…
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