AP EAMCET · Maths · Application of Derivatives
The number of tangent to the curve \(y^2(x-a)=x^2(x+a)(a>0)\) that are parallel to the \(X\)-axis is
- A infinitely many
- B 0
- C 1
- D 2
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Given, curve is \[ y^2(x-a)=x^2(x+a) \] Apply log on both sides \[ \begin{array}{ll} & \log \left\{y^2(x-a\}=\log \left\{x^2(x+a)\right\}\right. \\ \Rightarrow \quad & 2 \log y+\log (x-a)=2 \log x+\log (x+a) \end{array} \] Differentiating both sides w.r.t. \(x\), we get…
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