The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is
- $0^{\circ}$
- $60^{\circ}$
- $30^{\circ}$
- $15^{\circ}$
The Correct Option is B
Solution and Explanation
Angle between assymptotes is given by $2\tan^{-1} \left(\frac{b}{a}\right) = 2 \times30^{\circ} = 60^{\circ}$
Top Questions on Hyperbola
- If the line \( ax + 2y = 1 \), where \( a \in \mathbb{R} \), does not meet the hyperbola \( x^2 - 9y^2 = 9 \), then a possible value of \( a \) is:
- Let \( PQ \) be a chord of the hyperbola \[ \frac{x^2}{4} - \frac{y^2}{b^2} = 1, \] perpendicular to the \(x\)-axis such that \( OPQ \) is an equilateral triangle, \( O \) being the centre of the hyperbola. If the eccentricity of the hyperbola is \( \sqrt{3} \), then find the area of the triangle \( OPQ \).
- Let the foci of a hyperbola be \( (1, 14) \) and \( (1, -12) \). If it passes through the point \( (1, 6) \), then the length of its latus-rectum is:
- Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be $ 2a $ and $ 2b $, respectively, and one focus and the corresponding directrix of this hyperbola be $ (-5, 0) $ and $ 5x + 9 = 0 $, respectively. If the product of the focal distances of a point $ (\alpha, 2\sqrt{5}) $ on the hyperbola is $ p $, then $ 4p $ is equal to:
- If the normal drawn to the hyperbola \( xy = 16 \) at (8, 2) meets the hyperbola again at a point \((\alpha, \beta)\), then \( |\beta| + \frac{1}{|\alpha|} = \)
Questions Asked in COMEDK UGET exam
- Given that the freezing point of benzene is $ 5.48^\circ C $ and its $ K_f $ value is $ 5.12^\circ C/m $, what would be the freezing point of a solution of 20 g of propane in 400 g of benzene?
- COMEDK UGET - 2024
- Colligative Properties
200 ml of an aqueous solution contains 3.6 g of Glucose and 1.2 g of Urea maintained at a temperature equal to 27$^{\circ}$C. What is the Osmotic pressure of the solution in atmosphere units?
Given Data R = 0.082 L atm K$^{-1}$ mol$^{-1}$
Molecular Formula: Glucose = C$_6$H$_{12}$O$_6$, Urea = NH$_2$CONH$_2$- COMEDK UGET - 2024
- Colligative Properties
- An inorganic compound W undergoes the following reactions: $ W + \text{Na}_2\text{CO}_3 \xrightarrow{\text{O}_2 / \text{heat}} X + H^+ \xrightarrow{} Y(s) $ $ Y(aq) + \text{KCl} (aq) \xrightarrow{} Z(s) $ Z appears in the form of orange crystals and is used as an oxidising agent in acid medium. Identify the compound W.
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- coordination compounds
- A current of 3.0 A is passed through 750 ml of 0.45 M solution of CuSO₄ for 2 hours with a current efficiency of 90\%. If the volume of the solution is assumed to remain constant, what would be the final molarity of CuSO₄ solution?
- COMEDK UGET - 2024
- Solutions
- For a reaction $ 5X + Y \to 3Z $, the rate of formation of Z is $ 2.4 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} $. Calculate the average rate of disappearance of X.
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- Stoichiometry and Stoichiometric Calculations
Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
