AP EAMCET · Maths · Application of Derivatives
If the tangent to the curve \(x y+a x+b y=0\) at \((1,1)\) makes an angle \(\operatorname{Tan}^{-1} 2\) with X -axis, then \(\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}=\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx}(xy+ax+by) = 0\) \(y + x\frac{dy}{dx} + a + b\frac{dy}{dx} = 0\) \(\frac{dy}{dx} = -\frac{y+a}{x+b}\) \(m = \left.\frac{dy}{dx}\right|_{(1,1)} = -\frac{1+a}{1+b}\) \(m = \tan(\operatorname{Tan}^{-1} 2) = 2\)…
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