Conic Sections Class 12 Exercise has been updated according to the latest syllabus of 2080. It means the notes of Conic Section chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.
Chapter – 8
Conic Section
A hyperbola is a type of conic section that forms a symmetric curve with two separate branches. It is defined as the set of points where the absolute difference of distances from two fixed points (foci) is constant.
Properties of Hyperbola
- Foci: The foci are the fixed points inside each branch of the hyperbola, and the distance between them determines the shape of the curve.
- Vertices: The vertices are the points where the hyperbola intersects its transverse axis, and they lie on the major axis of the hyperbola.
- Asymptotes: Hyperbolas have asymptotes, which are straight lines that the curve approaches but never intersects.
Conic Sections Class 12 Exercise PDF
This PDF will provide the solutions of every question from the 5th exercise of class 12 conic section which contains the exercise related to hyperbola. If you want the solutions of other exercises then you can select the exercise from the button given above.
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Standard Equation of Hyperbola
The standard equation of a hyperbola centered at the origin is given by (\frac{x²}{a²) – \frac{y²}{b²} = 1) for a horizontal transverse axis and (\frac{y²}{b²)- \frac{x²}{a²} = 1) for a vertical transverse axis, where “a” and “b” are the distances from the center to the vertices.
Applications of Hyperbola
- Optics: Hyperbolas are used in designing satellite dishes, antennas, and telescopes to reflect signals or light waves.
- Navigation: Hyperbolic navigation is based on hyperbolic lines that intersect at right angles, allowing for precise location determination.
- Physics: Hyperbolas appear in celestial mechanics, such as the orbits of comets around the sun.
Understanding the properties and equations of hyperbolas is essential for solving geometric problems, analyzing conic sections, and exploring their applications in mathematics, physics, and engineering
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