MHT CET · Maths · Application of Derivatives
The equation of normal to the curve \(2 x^{2}+3 y^{2}-5=0\) at \(P(1,1)\) is
- A \(3 x+2 y+1=0\)
- B \(3 x-2 y+1=0\)
- C \(3 x+2 y-5=0\)
- D \(3 x-2 y-1=0\)
Answer & Solution
Correct Answer
(D) \(3 x-2 y-1=0\)
Step-by-step Solution
Detailed explanation
Given \(2 x^{2}+3 y^{2}-5=0\)
\(
4 x+6 y \frac{d y}{d x}=0 \Rightarrow \frac{d y}{d x}=\frac{-2 x}{3 y}
\)
\(\operatorname{At}(1,1), \quad \frac{\mathrm{d} y}{\mathrm{dx}}=\frac{-2}{3} \Rightarrow\) Slope of normal \(=\frac{3}{2}\) Equation of normal is
\(y-1=\frac{3}{2}(x-1) \Rightarrow 2 y-2=3 x-3\)
\(\therefore 3 x-2 y-1=0\)
\(
4 x+6 y \frac{d y}{d x}=0 \Rightarrow \frac{d y}{d x}=\frac{-2 x}{3 y}
\)
\(\operatorname{At}(1,1), \quad \frac{\mathrm{d} y}{\mathrm{dx}}=\frac{-2}{3} \Rightarrow\) Slope of normal \(=\frac{3}{2}\) Equation of normal is
\(y-1=\frac{3}{2}(x-1) \Rightarrow 2 y-2=3 x-3\)
\(\therefore 3 x-2 y-1=0\)
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
- A vector \(\bar{a}\) has components \(2 p\) and 1 with respect to a rectangular Cartesian system. This system is rotated though a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, à has components \(p+1\) and 1 , thenMHT CET 2022 Medium
- Given \(X \sim B(n, p)\), If \(E(X)=4\) and \(\operatorname{Var}(X)=2 \cdot 4\), then \(\mathrm{n}=\)MHT CET 2020 Easy
- \(\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} d x=\)MHT CET 2023 Easy
- \(\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=\)MHT CET 2021 Easy
- If \(P^{\prime}\left(A^{\prime}\right)+P\left(B^{\prime}\right) P(A \cup B)=0.7\) then \(P^{\prime}\left(A^{\prime}\right)+P\left(B^{\prime}\right)\) isMHT CET 2022 Medium
- For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set isMHT CET 2021 Medium
More PYQs from MHT CET
- When a rod of length \(l\) is rotated with angular velocity of \(\omega\) in a perpendicular field of induction \(B\), about one end, the emf across its ends isMHT CET 2010 Medium
- Maximum value of \(\mathrm{Z}=100 x+70 y\) Subject to \(2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0\) isMHT CET 2024 Easy
- What is the IUPAC name of the following compound?
MHT CET 2024 Hard - If \(x\) is real, then the difference between the greatest and least values of \(\frac{x^2-x+1}{x^2+x+1}\) isMHT CET 2025 Medium
- The magnetic susceptibility of iron is 5499. The relative permeability of iron will beMHT CET 2025 Easy
- If both mean and variance of 50 observations \(x_1, x_2, \ldots, x_{50}\) are equal to 16 and 256 respectively, then mean of \(\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots,\left(x_{50}-5\right)^2\) isMHT CET 2023 Hard