AP EAMCET · Maths · Application of Derivatives
The area (in square units) of the triangle formed by the X - axis, the tangent and the normal drawn at \((1,1)\) to the curve \(x^3+y^3=2 x y\) is
- A \(\frac{1}{2}\)
- B \(1\)
- C \(2\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
3x2+3y2dydx=2y+2xdydx\(3x^2+3y^2\frac{dy}{dx}=2y+2x\frac{dy}{dx}\) At (1,1):3+3dydx=2+2dydx⟹dydx=−1\( \text{At } (1,1): 3+3\frac{dy}{dx}=2+2\frac{dy}{dx} \implies \frac{dy}{dx}=-1 \) Tangent: y−1=−1(x−1)⟹y=−x+2\( \text{Tangent: } y-1=-1(x-1) \implies y=-x+2 \)…
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