AP EAMCET · Maths · Hyperbola
If the angle between the asymptotes of the hyperbola \(x^2-k y^2=3\) is \(\frac{\pi}{3}\) and \(e\) is its eccentricity, then the pole of the line \(x+y-1=0\) with respect to this hyperbola is
- A \(\left(k, \frac{\sqrt{3} e}{2}\right)\)
- B \(\left(-k, \frac{\sqrt{3} e}{2}\right)\)
- C \(\left(-k,-\frac{\sqrt{3} e}{2}\right)\)
- D \(\left(k,-\frac{\sqrt{3} e}{2}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(k,-\frac{\sqrt{3} e}{2}\right)\)
Step-by-step Solution
Detailed explanation
Given the equation of hyperbola is \(x^2-k y^2=3\) \(\Rightarrow \frac{x^2}{3}-\frac{y^2}{\frac{3}{k}}=1\) So, angle between the asymptotes is \(\theta=\tan ^{-1}\left(\frac{2 a b}{a^2-b^2}\right)\)…
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 differential equation corresponding to the family of parabolas \(y^2=4 a(x+a)\), where \(a\) is the parameter, isAP EAMCET 2018 Easy
- If \(\int \frac{\mathrm{dx}}{1-\sin ^4 \mathrm{x}}=\mathrm{A} \tan \mathrm{x}+\mathrm{B} \operatorname{Tan}^{-1}(\sqrt{2} \tan \mathrm{x})+\mathrm{C}\), then \(\mathrm{A}^2-\mathrm{B}^2=\)AP EAMCET 2025 Hard
- \(\lim _{x \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}}=\)AP EAMCET 2024 Easy
- If \(P(A \cup B)=0.8\) and \(P(A \cap B)=0.3\), then \(P(\bar{A})+P(\bar{B})\) is equal to:AP EAMCET 2003 Medium
- Find the equation of the parabola which passes through , has its vertex at the origin and its axis along the axis.AP EAMCET 2021 Easy
- The equation of the circle with \((1,1)\) as centre and which cuts a chord of length \(4 \sqrt{2}\) units on the line \(x+y+1=0\) isAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- The amplitude of the side bands of the modulated signal if the carrier signal and message signal amplitudes are \(25 \mathrm{~V}\) and \(5 \mathrm{~V}\) respectively isAP EAMCET 2022 Easy
- The number of solutions of the following system of linear homogeneous equations \(x-y+z=0, x+2 y-z=0\) and \(2 x+y+3 z=0\) isAP EAMCET 2021 Medium
- If \({ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3\), then the minimum value of \(n\) isAP EAMCET 2011 Easy
- If the mid-points of the sides \(B C, C A\) and \(A B\) of a triangle \(A B C\), are respectively \((2,1)\), \((-1,-2)\) and \((3,3)\), then the equation of the side \(B C\) isAP EAMCET 2019 Easy
- A solution of urea (molar mass ) boils at at the atmospheric pressure. if and for water are and respectively. The freezing point of the solution will beAP EAMCET 2021 Medium
- An electromagnetic radiation has an energy \(14.4 \mathrm{keV}\). To which region of the electromagnetic spectrum it belongs?AP EAMCET 2018 Easy