AP EAMCET · Maths · Hyperbola
If the angle between the asymptotes of a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is \(2 \operatorname{Tan}^{-1}\left(\frac{2}{3}\right)\) and \(\mathrm{a}^2-\mathrm{b}^2=45\), then \(\mathrm{ab}=\)
- A \(20\)
- B \(24\)
- C \(45\)
- D \(54\)
Answer & Solution
Correct Answer
(D) \(54\)
Step-by-step Solution
Detailed explanation
\(2 \operatorname{Tan}^{-1}\left(\frac{b}{a}\right) = 2 \operatorname{Tan}^{-1}\left(\frac{2}{3}\right) \implies \frac{b}{a} = \frac{2}{3}\) \(b = \frac{2}{3}a\) \(a^2 - b^2 = 45 \implies a^2 - \left(\frac{2}{3}a\right)^2 = 45\)…
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 denotes greatest integer function, thenAP EAMCET 2022 Medium
- The pole of the line with respect of the circle isAP EAMCET 2022 Medium
- If \(\mathrm{P}=(\overline{\mathrm{a}} \times \overline{\mathrm{i}})^2+(\overline{\mathrm{a}} \times \overline{\mathrm{j}})^2+(\overline{\mathrm{a}} \times \overline{\mathrm{k}})^2\) and \(\mathrm{Q}=(\overline{\mathrm{a}} \cdot \overline{\mathrm{i}})^2+(\overline{\mathrm{a}} \cdot \overline{\mathrm{j}})^2+(\overline{\mathrm{a}} \cdot \overline{\mathrm{k}})^2\), thenAP EAMCET 2025 Medium
- A and B are mutually exclusive events of a random experiment and \(\mathrm{P}(\mathrm{B}) \neq 1\), then \(\mathrm{P}\left(\mathrm{A} \mid \mathrm{B}^{\mathrm{C}}\right)=\)AP EAMCET 2023 Easy
- If \(c\) and \(d\) are the roots of \(x^2+a x+b=0\), then a root of \(x^2+(4 c+a) x+\left(b+2 a c+4 c^2\right)=0\) isAP EAMCET 2023 Medium
- The maximum value of the function \(f(x)=\tan \left(x+\frac{2 \pi}{3}\right)\)
\(-\tan \left(x+\frac{\pi}{6}\right)+\cos \left(x+\frac{\pi}{6}\right)\) in \(\left[-\frac{5 \pi}{12}, \frac{-\pi}{3}\right]\) isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- If the solution of the system of simultaneous linear equations \(x+y-z=6,3 x+2 y-z=5\) and \(2 x-y-2 z+\) \(3=0\) is \(x=\alpha, y=\beta, z=\gamma\), then \(\alpha+\beta=\)AP EAMCET 2024 Medium
- If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting tail on both the coins isAP EAMCET 2023 Easy
- If the directrix of the parabola \(x^2+4 y-6 x+\lambda=0\) is \(y+1=0\), then which of the following is correct?AP EAMCET 2022 Easy
- The maximum velocity of an electron emitted by light of wavelength \(\lambda\) incident on the surface of a metal of work function \(\phi\) is [ \(h=\) Planck's constant, \(m=\) mass of electron and \(c=\) speed of light]AP EAMCET 2020 Medium
- If \(A=\left[\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right]\) and \(A^{-1}=\left[\begin{array}{cc}a+i b & -c-i d \\ -c+i d & a-i b\end{array}\right]\). Find \(\left(a^2+b^2+c^2+d^2\right)\).AP EAMCET 2020 Easy
- If \(\mathrm{A}=\left\{\mathrm{x} / 9 \mathrm{x} \geq \mathrm{x}^2+20\right\}\) and \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}\) is defined by \(f(x)=2 x^3-15 x^2+36 x-48\), then the maximum value of \(f(x)\) isAP EAMCET 2023 Medium