MHT CET · Maths · Application of Derivatives
The equation of tangent at \(\mathrm{P}(-4,-4)\) on the curve \(x^{2}=-4 y\) is
- A 2x+y+4=0
- B 2x-y+4=0
- C 2x+y-4=0
- D 3x-y+8=0
Answer & Solution
Correct Answer
(B) 2x-y+4=0
Step-by-step Solution
Detailed explanation
(D)
We have \(x^{2}=-4 y \Rightarrow 2 x=-4 \frac{d y}{d x} \Rightarrow \frac{d y}{d x}=\frac{-x}{2}\)
Hence slope of tangent at \(P(-4,-4)\) is 2 . Hence required eq. of tangent is \(y+4=2(x+4) \quad \Rightarrow 2 x-y+4=0\)
We have \(x^{2}=-4 y \Rightarrow 2 x=-4 \frac{d y}{d x} \Rightarrow \frac{d y}{d x}=\frac{-x}{2}\)
Hence slope of tangent at \(P(-4,-4)\) is 2 . Hence required eq. of tangent is \(y+4=2(x+4) \quad \Rightarrow 2 x-y+4=0\)
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
- \(A\) rod \(A B, 13\) feet long moves with its ends \(A\) and \(B\) on two perpendicular lines \(O X\) and \(O Y\) respectively. When \(\mathrm{A}\) is 5 feet from \(\mathrm{O}\), it is moving away at the rate of \(3 \mathrm{feet} / \mathrm{sec}\). At this instant, B is moving at the rateMHT CET 2023 Medium
- The centroid of tetrahedron with vertices \(\mathrm{P}(5,-7,0), \mathrm{Q}(\mathrm{a}, 5,3), \mathrm{R}(4,-6, \mathrm{~b})\) and \(\mathrm{S}(6, \mathrm{c}, 2)\) is \((4,-3,2)\), then the value of \(2 a+3 b+c\) is equal toMHT CET 2024 Medium
- The derivative of \(\mathrm{f}(\sec x)\) with respect to \(\mathrm{g}(\tan x)\) at \(x=\frac{\pi}{4}\), where \(\mathrm{f}^{\prime}(\sqrt{2})=4\) and \(\mathrm{g}^{\prime}(1)=2\), isMHT CET 2023 Easy
- If \(\mathrm{g}(x)=[\mathrm{f}(2 \mathrm{f}(x)+2)]^2\) and \(\mathrm{f}(0)=-1, \mathrm{f}^{\prime}(0)=1\), then \(g^{\prime}(0)\) isMHT CET 2024 Easy
- If \(y=\mathrm{A} \cos \mathrm{n} x+\mathrm{B} \sin \mathrm{n} x\), then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=\)MHT CET 2024 Easy
- Let \(\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]\) and \(\mathrm{A}^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}, \alpha, \beta \in \mathbb{R}\), I is the identity matrix of order 2 , then \(4(\alpha-\beta)\) isMHT CET 2024 Easy
More PYQs from MHT CET
- N-ethyl-N-methylpropan-1-amine isMHT CET 2010 Easy
- If ‘x’, ‘v’ and ‘a’ denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time t, then which one of the following does not change with time?MHT CET 2019 Easy
- A particle of charge ' \(\mathrm{q}\) ' and mass ' \(\mathrm{m}\) ' moves in a circular orbit of radius ' \(r\) ' with angular speed ' \(\omega\) '. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends onMHT CET 2021 Easy
- Identify the product obtained when nitro ethane is treated with \(\mathrm{Sn}-\mathrm{HCl}\) under ideal conditions.MHT CET 2025 Easy
- In incomplete dominance each of the parental traits reappears in the \(F _2\) generation by _________ %.MHT CET 2020 Medium
- The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom isMHT CET 2023 Medium