AP EAMCET · Maths · Application of Derivatives
If two curves \(x=y^2, x y=a^3\) cut each other orthogonally at a point, then \(a^2\) is equal to
- A \(\frac{1}{3}\)
- B \(\frac{1}{2}\)
- C 2
- D 3
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(x=y^2\) and \(x y=a^3\) Solving, we get \[ x=a^2 \text { and } y=a \] Now, \(y^2=x\)…
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
- A homogeneous equation of second degree in \(x\) and \(y\) represents which of the following?AP EAMCET 2020 Easy
- For \(-1 < x < 1\), if \(f(x)=\cos ^2\left(\tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right)\), then \(f^{\prime}(x)=\)AP EAMCET 2018 Medium
- If \(y=\log _e \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\), then \(\tanh \left(\frac{y}{2}\right)=\)AP EAMCET 2019 Medium
- If \(\alpha_1, \alpha_2, \ldots, \alpha_{23}\) are the 23 rd roots of unity, then \(\alpha_1^{47}+\alpha_2^{47}+\ldots .+\alpha_{23}^{47}=\)AP EAMCET 2022 Medium
- Solve the following differential equation
\[
\left(x^2+1\right) \frac{d y}{d x}+4 x y=\frac{1}{x^2+1}
\]AP EAMCET 2021 Easy - The product of the perpendicular distances drawn from any point on the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) to its asymptotes isAP EAMCET 2017 Hard
More PYQs from AP EAMCET
- At \(300 \mathrm{~K}, \mathrm{PCl}_{5(g)} \rightleftharpoons \mathrm{PCl}_{3(g)}+\mathrm{Cl}_{2(g)}\) and \(K_p=1.8 \times 10^{-7}\). Then calculate its \(\Delta G^0\).AP EAMCET 2020 Hard
- If \(x\) is real, then the value of \(\frac{x^2-3 x+4}{x^2+3 x+4}\) lies in the intervalAP EAMCET 2011 Medium
- The equivalent capacitance between the points \(\mathrm{A}\) and \(\mathrm{B}\) of the network shown in the figure is
AP EAMCET 2017 Easy - In which of the following, reagent and product are correctly matched with respect to benzene diazonium chloride as reactant?AP EAMCET 2023 Medium
- Which one of the following is an anionic detergent?AP EAMCET 2017 Easy
- If is such that , thenAP EAMCET 2022 Easy