AP EAMCET · Maths · Application of Derivatives
Find the equation of normal to the curve \(y=x^3-3 x\), which is parallel to the line \(2 x+18 y=9\) ?
- A \(x+9 y=20\) only
- B \(x+9 y=40\) only
- C \(x+9 y= \pm 20\)
- D \(x+9 y= \pm 40\)
Answer & Solution
Correct Answer
(C) \(x+9 y= \pm 20\)
Step-by-step Solution
Detailed explanation
Given, line is \(2 x+18 y=9\) \[ \begin{gathered} \text { slope }(m)=\frac{-a}{b} \\ m=\frac{-2}{18}=-\frac{1}{9} \end{gathered} \] Given equation of curve is \[ y=x^3-3 x \] Differentiate w.r.to ' \(x\) ', we get \[ \frac{d y}{d x}=3 x^2-3 \] \(\therefore\) Slope of normal…
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