TS EAMCET · Maths · Hyperbola
If the product of the perpendicular distances from any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) to its asymptotes is \(\frac{36}{13}\) and its eccentricity is \(\frac{\sqrt{13}}{3}\), then \(a-b=\)
- A \(4\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(d_1 d_2 = \frac{a^2b^2}{a^2+b^2}\) \(\frac{a^2b^2}{a^2+b^2} = \frac{36}{13}\) \(e^2 = 1 + \frac{b^2}{a^2}\) \(\left(\frac{\sqrt{13}}{3}\right)^2 = 1 + \frac{b^2}{a^2}\) \(\frac{13}{9} = 1 + \frac{b^2}{a^2}\) \(\frac{b^2}{a^2} = \frac{4}{9} \implies b = \frac{2}{3}a\)…
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
- Number of triangles whose vertices are the points \((x, y)\) in the XY-plane with integer coordinates satisfying \(0 \leq x \leq 4\) and \(0 \leq y \leq 4\) isTS EAMCET 2025 Hard
- \(\int \sqrt{\frac{2+x}{2-x}} d x\) is equal toTS EAMCET 2015 Easy
- If \(\mathrm{A}(1,1), \mathrm{B}(-1,1)\) and \(\mathrm{C}(-1,-1)\) are three points and a point \(\mathrm{P}\) moves such that \(\mathrm{PA}^2=\mathrm{PB}^2+\mathrm{PC}^2\), then the equation of the locus of \(\mathrm{P}\) isTS EAMCET 2022 Medium
- A box contains 10 mangoes out of which 4 are spoiled. 2 mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, isTS EAMCET 2019 Medium
- \(\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=\)TS EAMCET 2023 Medium
- If the tangent and normal drawn to the curve \(x=a(\theta+\sin \theta), y=a(1-\cos \theta)\) at \(P\left(\theta=\frac{\pi}{2}\right)\) cuts the \(\mathrm{X}\)-axis at \(A\) and \(B\) respectively, then the area (in sq. units) of \(\triangle P A B\) isTS EAMCET 2020 Medium
More PYQs from TS EAMCET
- The number of normals that can be drawn through the point \((9,6)\) to the parabola \(y^2=4 x\) isTS EAMCET 2024 Medium
- A gas is at constant pressure \(4 \times 10^5 \mathrm{~N} / \mathrm{m}^2\). When a heat energy of \(2000 \mathrm{~J}\) is supplied to the gas, its volume changes by \(3 \times 10^{-3} \mathrm{~m}^3\). What is the increase in its internal energy?TS EAMCET 2020 Easy
- A body centred cubic lattice is made up of two different types of atoms X and Y. Atom X occupies the body centre and atoms \(\mathrm{Y}\) occupy the corner positions. One of the corners is left unoccupied per unit cell. The empirical formula of it isTS EAMCET 2023 Medium
- Which of the following statements about \(\mathrm{BF}_4^{-}\) and \(\mathrm{AlF}_6^{3-}\) are correct? (i) \(\mathrm{B}\) and \(\mathrm{Al}\) differ in their oxidation states. (ii) \(\mathrm{B}\) and \(\mathrm{Al}\) differ in their covalency. (iii) B obeys the octet rule. (iv) \(\mathrm{B}\) and \(\mathrm{Al}\) are in diagonal relationship.TS EAMCET 2018 Easy
- In a triangle, if \(b=20, c=21\) and \(\sin A=\frac{3}{5}\), then \(a\) is equal to :TS EAMCET 2003 Easy
- \(\frac{d}{d t}\left(\tan t+t^2 \operatorname{cosec} h t\right)\) is equal toTS EAMCET 2021 Medium