Question:
The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is
The angle between the asymptotes of the hyperbola $x^2 - 3y^2 = 12$ is
Updated On: May 12, 2024
- $0^{\circ}$
- $60^{\circ}$
- $30^{\circ}$
- $15^{\circ}$
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The Correct Option is B
Solution and Explanation
We have $x^2 - 3y^2 = 12 \Rightarrow \:\:\: \frac{x^{2}}{12} - \frac{y^{2}}{4} = 1 $
Angle between assymptotes is given by $2\tan^{-1} \left(\frac{b}{a}\right) = 2 \times30^{\circ} = 60^{\circ}$
Angle between assymptotes is given by $2\tan^{-1} \left(\frac{b}{a}\right) = 2 \times30^{\circ} = 60^{\circ}$
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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.
