TS EAMCET · Maths · Parabola
Match the points on the curve \(2 y^2=x+1\) with the slopes of normals at those points and choose the correct answer. 
- A \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \ 2 & 4 & 3 & 1\end{array}\)
- B \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \ 2 & 5 & 3 & 1\end{array}\)
- C \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \ 2 & 3 & 5 & 1\end{array}\)
- D \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \ 2 & 5 & 1 & 3\end{array}\)
Answer & Solution
Correct Answer
(B) \(\begin{array}{llll}\text { A } & \text { B } & \text { C } & \text { D } \ 2 & 5 & 3 & 1\end{array}\)
Step-by-step Solution
Detailed explanation
Given equation of curve is \[ 2 y^2=x+1 \] On differentiating both sides w.r.t. \(x\), we get \[ \text { 4y } \frac{d y}{d x}=1 \Rightarrow \frac{d y}{d x}=\frac{1}{4 y} \] \(\therefore\) The slope of the normal is \[ \frac{d x}{d y}=-4 y \] I.…
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
- \(\int\left(\frac{\left(\sin ^4 x+2 \cos ^2 x-1\right) \cos x}{(1+\sin x)^6}\right) d x=\)TS EAMCET 2024 Hard
- TS EAMCET 2021 Easy
- If sum of the coefficients of \(x^r(r=0,1,2, \ldots, 2 n)\) in the expansion of \(\left(1+3 x-2 x^2\right)^n\) is 128 , then \(\sum_{r=1}^{2 n} r \frac{(2 n)_{C_r}}{(2 n)_{C_{r-1}}}=\)TS EAMCET 2020 Hard
- If \(\cosh ^{-1}\left(\frac{5}{3}\right)+\sinh ^{-1}\left(\frac{3}{4}\right)=k\), then \(e^k=\)TS EAMCET 2024 Easy
- The general solution of the equation \((\sqrt{3}-1) \sin \theta+(\sqrt{3}+1) \cos \theta=2\) isTS EAMCET 2020 Easy
- The equation of the normal to the curve \(y^4=a x^3\) at \((a, a)\) isTS EAMCET 2008 Easy
More PYQs from TS EAMCET
- If the position vectors of \(A, B\) and \(C\) are respectively \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\), then \(\cos ^2 A\) is equal toTS EAMCET 2008 Medium
- If \((2,-1,3)\) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane isTS EAMCET 2023 Medium
- The degree of ionization of \(0.10 \mathrm{M}\) lactic acid is \(4.0 \%\)
The value of \(K_c\) isTS EAMCET 2013 Medium - Paracetamol isTS EAMCET 2020 Easy
- The difference in the wavelength between the maximum and minimum of Balmer series [Use \(\mathrm{R}_{\mathrm{H}}=1 \times 10^7 \mathrm{~m}^{-1}\) ]TS EAMCET 2022 Easy
- If \(m\) and \(\mathrm{M}\) are respectively the smallest and greatest rational roots of the equation \(6 x^6-25 x^5+31 x^4-31 x^2+25 x-6=0\), then \(\mathrm{M}-m=\)TS EAMCET 2022 Easy