TS EAMCET · Maths · Application of Derivatives
\(\mathrm{P}(5,2)\) is a point on the curve \(y=f(x)\) and \(\frac{7}{2}\) is the slope of the tangent to the curve at P. The area of the triangle (in sq. units) formed by the tangent and the normal to the curve at P with \(x\)-axis is
- A \(35\)
- B \(\frac{35}{2}\)
- C \(\frac{53}{7}\)
- D \(\frac{53}{14}\)
Answer & Solution
Correct Answer
(C) \(\frac{53}{7}\)
Step-by-step Solution
Detailed explanation
Tangent at \(P(5,2)\): \(y-2 = \frac{7}{2}(x-5) \Rightarrow 7x-2y-31=0\). X-intercept: \(x_T = \frac{31}{7}\). Normal at \(P(5,2)\): \(m_N = -\frac{2}{7} \Rightarrow y-2 = -\frac{2}{7}(x-5) \Rightarrow 2x+7y-24=0\). X-intercept: \(x_N = 12\). Base of triangle…
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
- The variance of the following continuous frequency distribution is \(\begin{array}{|l|c|c|c|c|}\hline \text{Class interval} & 0-4 & 4-8 & 8-12 & 12-16 \\hline \text{Frequency} & 2 & 3 & 2 & 1 \\hline\end{array}\)TS EAMCET 2024 Easy
- , where denotes GIFTS EAMCET 2021 Easy
- If \(f:[1, \infty) \rightarrow[0, \infty)\) is given by \(f(x)=x-\frac{1}{x}\), then \(f^{-1}(x)=\)TS EAMCET 2019 Easy
- If the possible solution of the equation \(2 \cos ^2 x+3 \sin x-3=0\) constitute two unequal angles of a triangle, then the third angle of that triangle isTS EAMCET 2020 Easy
- If \(A\) and \(B\) are independent events of a random experiment such that \(P(A \cap B)=\frac{1}{6}\) and \(P(\bar{A} \cap \bar{B})=\frac{1}{3}\), then \(P(A)\) is equal to (Here, \(\overrightarrow{\mathbf{E}}\) is the complement of the event \(E\) )TS EAMCET 2008 Medium
- The derivate of with respect to at isTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- Heat loss takes place from a body maintained at a temperature of \(400^{\circ} \mathrm{C}\) to the surrounding air at \(30^{\circ} \mathrm{C}\) by convection and to the surrounding surfaces at \(30^{\circ} \mathrm{C}\) by radiation. The Newton's cooling coefficient is \(20 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}\) and the Stefan-Boltzmann constant is \(5.67 \times 10^{-8}\) \(\mathrm{W} / \mathrm{m}^2 \mathrm{~K}^4\). If the rate of heat loss by convection is equal to the rate of heat loss by radiation, the emissivity of the body surface isTS EAMCET 2018 Medium
- A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the stopping distance is \(S_1\). The man returns home on the same scooter, with the same speed with a 60 kg bag of rice. If \(S_2\) is the new stopping distance when the brakes are applied with the same force, thenTS EAMCET 2024 Medium
- If the altitude of a triangle are in arithmetic progression, then the sides of the triangles are inTS EAMCET 2002 Medium
- A straight line makes an intercept on the \(Y\)-axis twice as long as that on \(X\)-axis and is at unit distance from the origin. Then the line is represented by the equationsTS EAMCET 2017 Medium
- If \(x=\alpha, y=\beta, z=\gamma\) is the solution of the system of equations \(2 x+3 y+z=-1\), \(3 x+y+z=4, x-3 y-2 z=1\), then the value of \(\beta\) isTS EAMCET 2025 Medium
- The need for modulation isTS EAMCET 2023 Easy