TS EAMCET · Maths · Application of Derivatives
If \(A=\left\{P(\alpha, \beta) /\right.\) the tangent drawn at \(P\) to the curve \(y^3-3 x y\) \(+2=0\) is a horizontal line \(\}\) and \(B=\{Q(a, b) /\) the tangent drawn at Q to the curve \(y^3-3 x y+2=0\) is a vertical line \} then \(n(A)+n(B)=\)
- A 12
- B 1
- C 0
- D 4
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
Given curve : \(y^3-3 x y+2=0\) \(\frac{d y}{d x}=\frac{y}{y^2-x}\) For vertical tangent \(\frac{d y}{d x}=\infty \Rightarrow y^2-x=0\) \(\Rightarrow y^2=x \Rightarrow n(B)=1\) For horizontal tangent \(\frac{d y}{d x}=0\) \(\Rightarrow y=0\) \(\quad\)[Does not satisfies given…
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