AP EAMCET · Maths · Hyperbola
Let \(x^2+y^2=16\) be the equation of the auxiliary circle of a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and let \((4 \sqrt{2}, 3)\) be a point on the hyperbola. Then, the eccentricity of the hyperbola is
- A \(5 / 4\)
- B \(5 / 3\)
- C \(4 / 3\)
- D 2
Answer & Solution
Correct Answer
(A) \(5 / 4\)
Step-by-step Solution
Detailed explanation
The auxiliary circle of a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is \(x^2+y^2=a^2\). \[ \therefore \quad a^2=16 \Rightarrow a=4 \] The hyperbola passes through \((4 \sqrt{2}, 3)\)…
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 equation of the common tangent drawn to the curves \(y^2=8 x\) and \(x y=-1\) isAP EAMCET 2016 Medium
- If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) then the magnitude of the projection on \(\mathbf{c}\) of a unit vector that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) isAP EAMCET 2019 Easy
- If are the roots of , then ? (approximately close to)AP EAMCET 2021 Medium
- The value of ' \(k\) ' so that the line \(y=2 x+k\) may touch the ellipse \(3 x^2+5 y^2=15\) isAP EAMCET 2020 Easy
- If \(\mathrm{X} \sim \mathrm{B}(9, \mathrm{p})\) is a binomial variate satisfying the equation \(\mathrm{P}(\mathrm{x}=3)=\mathrm{P}(\mathrm{x}=6)\), then \(\mathrm{P}(\mathrm{x} < 3)=\)AP EAMCET 2025 Medium
- If \(y=\tan ^{-1} \frac{x}{1+2 x^2}+\tan ^{-1} \frac{x}{1+6 x^2}+\tan ^{-1} \frac{x}{1+12 x^2}\), then \(\left(\frac{d y}{d x}\right)_{x=\frac{1}{2}}=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- Observe the following species
\(\mathrm{AlCl}_3, \mathrm{NH}_3, \mathrm{H}^{+}, \mathrm{Co}^{3+},-\mathrm{OH}, \mathrm{H}^{-} \mathrm{Mg}^{2+}, \mathrm{BF}_3, \mathrm{Cl}^{-}\)
How many Lewis bases are present in the above list?AP EAMCET 2023 Easy - Which of the following statements is not correct?
1. Reduction of alumina to give aluminium by magnesium is thermodynamically feasible.
2. The point of intersection of \(\mathrm{AlO}_3\) and \(\mathrm{MgO}\) curves in Ellingham diagram is below \(1665 \mathrm{~K}\).
3. Use of magnesium as reducing agent in metallurgy of aluminium is economical.
4. Ellingham diagram represents the graphical plot of Gibbs energy vs temperature for the formation of the oxides of common metals and reducing agents.AP EAMCET 2020 Medium - If \(k \in N\) then \(\lim _{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots+\frac{1}{k n}\right]=\)AP EAMCET 2025 Medium
- In \(\triangle A B C\), if \(D\) and \(E\) are the mid-points of the sides \(B C\) and \(C A\) respectively, then \(2(\mathbf{A D}+\mathbf{E B})=\)AP EAMCET 2018 Easy
- The sum of all possible numbers that can be formed by using the digits \(2,3,5,7\) without repetition of digits isAP EAMCET 2022 Medium
- What is coordination of the metal inAP EAMCET 2021 Easy