TS EAMCET · Maths · Differential Equations
The equation of any member of the family of all the ellipses whose axes are along the coordinate axes satisfies the differential equation
- A \(x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0\)
- B \(x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y=y^{\prime}\)
- C \(y^{\prime \prime}+\frac{\left(y^{\prime}\right)^2}{y}-\frac{y}{x}=0\)
- D \(y^{\prime \prime}+\left(y^{\prime}\right)^2+x^2 y^2=0\)
Answer & Solution
Correct Answer
(A) \(x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0\)
Step-by-step Solution
Detailed explanation
General equation of ellipse is \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) Differentiate w.r.t ' \(x\) '.…
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 \(\left(x^2-3 x+2\right) e^{\frac{y}{x-1}}=x+2\) then \(\left(\frac{d y}{d x}\right)_{x=0}=\)TS EAMCET 2025 Medium
- Suppose \(\alpha, \beta, \gamma\) are the roots of \(x^3+x^2+x+2=0\). Then, the value of \(\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)\) isTS EAMCET 2015 Easy
- Let \(\mathrm{L}\) be a line passing through a point \(\mathrm{A}\) and parallel to the vector \(2 \hat{i}+\hat{j}-2 \hat{k}\). Let \(-7 \hat{i}-5 \hat{j}+11 \hat{k}\) be the position vector of a point \(\mathrm{P}\) on \(\mathrm{L}\) such that \(|\overline{\mathrm{AP}}|=12\). Then the position vector of A can beTS EAMCET 2022 Easy
- If \(P\) is \((3,1)\) and \(Q\) is a point on the curve \(y^2=8 x\), then the locus of the mid-point of the line segment \(P Q\) isTS EAMCET 2018 Easy
- Let . If is a relative maximum of at , thenTS EAMCET 2019 Medium
- If \(A=\left[\begin{array}{ll}0 & 5 \\ 0 & 0\end{array}\right]\) and \(f(x)=x+x^2+\ldots+x^{2018}\), then \(f(A)+I=\)TS EAMCET 2019 Easy
More PYQs from TS EAMCET
- I. Two non-zero, non-collinear vectors are linearly independent. II. Any three coplanar vectors are linearly dependent. Which of the above statements is/are true?TS EAMCET 2005 Easy
- The hybridizations of the central atom in the molecules \(\mathrm{BF}_3, \mathrm{BeF}_2, \mathrm{BrF}_3\) are respectivelyTS EAMCET 2023 Medium
- If the tangent drawn at the point \(\mathrm{P}(3 \sqrt{2}, 4)\) on the hyperbola \(\frac{x^2}{9}-\frac{y^2}{16}=1\) meets its directrix at \(Q(\alpha, \beta)\) in fourth quadrant then \(\beta=\)TS EAMCET 2025 Medium
- 4 different pairs of lines are given in List I and the cosine of the angle between every pair of lines is given in List II. Match the following:
The correct match is \(\text { A } \quad \text { B } \quad \text { C } \quad \text { D }\)TS EAMCET 2022 Easy - One mole of fluorine is reacted with two moles of hot concentrated \(\mathrm{KOH}\). The products formed are \(\mathrm{KF}, \mathrm{H}_2 \mathrm{O}\) and \(\mathrm{O}_2\). The molar ratio of \(\mathrm{KF}, \mathrm{H}_2 \mathrm{O}\) and \(\mathrm{O}_2\), respectively isTS EAMCET 2002 Hard
- A bullet of mass moving horizontally with speed hits a wooden block of mass that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height then how much of the initial kinetic energy of the bullet is lost in the collision?TS EAMCET 2020 Medium