TS EAMCET · Maths · Hyperbola
If \((8,2)\) is a point on the hyperbola whose length of the transverse axis is 12 and conjugate axis is \(x=0\), then the eccentricity of that hyperbola is
- A \(\frac{2 \sqrt{2}}{7}\)
- B \(\frac{8}{5}\)
- C \(\frac{2 \sqrt{2}}{\sqrt{7}}\)
- D \(\frac{\sqrt{8}}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{2 \sqrt{2}}{\sqrt{7}}\)
Step-by-step Solution
Detailed explanation
Let assume equation of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) Given that length of transverse axis, \(2 a=12\) or \(a=6\) \(\because\) Point \((8,2)\) lies on hyperbola, then it must satisfy the equation of hyperbola i.e., \(\frac{(8)^2}{a^2}-\frac{(2)^2}{b^2}=1\) or…
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 \(z=x+i y\) represents a point \(P\) in the argand plane, then the area of the region represented by the inequality \(2 < |z-(1+i)| < 3\) isTS EAMCET 2019 Easy
- 68. If \(f(x)=\frac{e^{-x} \sin x}{\log _e x}\) and \(f^{\prime}(x)=f(x) . g(x)\), then \(g^{\prime}(\mathrm{e})=\)
(a) \(e^{-2}-\operatorname{cosec}^2(e)\)
(b) \(2 e^{-2}-\operatorname{cosec}^2(e)\)
(c) \(2 e^{-2}-\operatorname{cosec}^2(e)\)
(d) \(2 e^{-2}+\operatorname{cosec}^2(e)\)TS EAMCET 2022 Easy - \(\int_0^{\pi / 4} x^2 \sin 2 x d x=\)TS EAMCET 2025 Medium
- If \(f(x)=\frac{(x+1) \sinh x}{e^{2 x} \tan x}\) and \(\frac{f^{\prime}(x)}{f(x)}=\frac{1}{x+1}+\operatorname{coth} x+g(x)\), then \(g(x)=\)TS EAMCET 2020 Hard
- Let \(S\) be the set of points on \(X\)-axis lying at a distance of \(d\) units from \((3,4)\). Which of the following is true?TS EAMCET 2021 Easy
- If is continuous at , thenTS EAMCET 2018 Easy
More PYQs from TS EAMCET
- Which of the following carbohydrates has a glycosidic linkage?TS EAMCET 2018 Easy
- For an ideal gas at a temperature of \(27^{\circ} \mathrm{C}\) and at constant pressure, the coefficient of volume expansion is nearlyTS EAMCET 2023 Easy
- A student has to answer a multiple-choice question having 5 alternatives in which two or more than two alternatives are correct. Then the number of ways in which the student can answer that question isTS EAMCET 2025 Medium
- Let \(\mathbb{N}\) be the set of positive integers. The number of distinct triplets \((x, y, z)\) satisfying \(x, y, z \in \mathbb{N}, x < y < z\) and \(x+y+z=12\) isTS EAMCET 2022 Easy
- If the angle between the asymptotes of a hyperbola is \(30^{\circ}\) then its eccentricity isTS EAMCET 2023 Medium
- Consider the following statements \(A\) and \(B\) and identify the correct answer A. When a person walks on a rough surface the direction of frictional force exerted by the surface on the person is opposite to the direction of his motion. B. When a cycle is in motion, the force of friction exerted by the ground on the front wheel is in the backward directionTS EAMCET 2004 Medium