AP 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…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If thenAP EAMCET 2018 Medium
- If \({ }^n C_7={ }^n C_6\), then \({ }^n C_2=\)AP EAMCET 2020 Easy
- In a \(\triangle A B C\), if \(\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\), then \(\triangle A B C\) isAP EAMCET 2011 Medium
- The area (in sq. units) of the region bounded by the curves \(y=4|\cos x|\) and \(y=-|\cos x|\) from \(x=-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) isAP EAMCET 2023 Medium
- The equations of lines parallel to the coordinate axes and passing through point \((5,-6)\) areAP EAMCET 2020 Easy
- Suppose \(A\) and \(B\) are two events such that \(P(A \cap B)=\frac{3}{25}\) and \(P(B-A)=\frac{8}{25} . \quad\) Then, \(P(B)\) is equal toAP EAMCET 2010 Easy
More PYQs from AP EAMCET
- The rank of the matrix is thenAP EAMCET 2021 Easy
- Find the Young's modulus of the wire whose stress-strain curve is as shown in the following figure
AP EAMCET 2021 Medium - Which of the following metals cannot be obtained by auto-reduction of their compounds?AP EAMCET 2020 Medium
- Finkelstein reaction is used for the synthesis ofAP EAMCET 2022 Easy
- If the line \(x+2 y=k\) intersects the curve \(x^2-x y+y^2+3 x+3 y-2=0\) at two points \(A\) and \(B\) and if \(O\) is the origin, then the condition for \(\angle \mathrm{AOB}=90^{\circ}\) isAP EAMCET 2018 Medium
- Let \(x \in R\) and \(\log _2 x>0\). Then, the vectors \(\mathbf{A}=\left(2, \log _2 x, s\right)\) and \(\mathbf{B}=\left(\log _2 x, s, \log _2 x\right)\) include an acute angle ifAP EAMCET 2021 Medium