TS EAMCET · Maths · Application of Derivatives
The equation of the normal to the curve \(y^4=a x^3\) at \((a, a)\) is
- A \(x+2 y=3 a\)
- B \(3 x-4 y+a=0\)
- C \(4 x+3 y=7 a\)
- D \(4 x-3 y=0\)
Answer & Solution
Correct Answer
(C) \(4 x+3 y=7 a\)
Step-by-step Solution
Detailed explanation
Given curve is \(y^4=a x^3\) On differentiating w.r.t. \(x\), we get \[ \begin{aligned} & 4 y^3 \frac{d y}{d x}=3 a x^2 \\ & \Rightarrow \quad\left(\frac{d y}{d x}\right)_{(a, a)}=\frac{3 a^3}{4 a^3}=\frac{3}{4} \\ & \end{aligned} \] \(\therefore\) Equation of normal at point…
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