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Equation Of Hyperbola Video Lecture | Mathematics (Maths) for JEE Main & Advanced

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FAQs on Equation Of Hyperbola Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is the general equation of a hyperbola?
Ans. The general equation of a hyperbola is $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center of the hyperbola, and $a$ and $b$ are the distances from the center to the vertices along the x-axis and y-axis respectively.
2. How do you determine the foci of a hyperbola from its equation?
Ans. To determine the foci of a hyperbola from its equation, you can use the formula $c = \sqrt{a^2 + b^2}$, where $c$ represents the distance from the center to the foci.
3. What is the difference between a horizontal and a vertical hyperbola?
Ans. In a horizontal hyperbola, the transverse axis is along the x-axis, while in a vertical hyperbola, the transverse axis is along the y-axis. This affects the placement of the vertices and the foci.
4. How can you identify the type of hyperbola from its equation?
Ans. The type of hyperbola can be identified by looking at the signs in the equation. If the x-term is positive, it is a horizontal hyperbola, and if the y-term is positive, it is a vertical hyperbola.
5. How do you find the asymptotes of a hyperbola?
Ans. The asymptotes of a hyperbola can be found using the formula $y = \pm \frac{b}{a}x + k$, where $a$ and $b$ are the distances from the center to the vertices along the x-axis and y-axis respectively, and $(h,k)$ is the center of the hyperbola.
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