The word “hyperbola” comes from the Greek o, which means “overthrown” or “extreme,” and is also the source of the English term hyperbole. Menaechmus discovered hyperbolae while investigating the problem of doubling the cube, but they were initially referred to as sections of obtuse cones. In his definitive treatise on conic sections, the C, Apollonius of Perga (c. 262–c. 190 BC) is thought to have created hyperbola. The ellipse and parabola, the other two general conic sections, are named after the Greek words for “deficient” and “applied,” respectively; all three names are derived from Pythagorean terminology that related to a comparison of the side of fixed-area rectangles with a specified line segment.
A hyperbola is a locus of a point in the plane with a constant ratio of the distance between the two fixed locations called foci. A mirror image of a parabola is known as a hyperbola. This article thoroughly explains the important properties of the hyperbola.
A hyperbola is generated when a right circular cone crosses a plane in such a way that the angle between the plane and the vertical axis is less than the vertical angle. The plane cuts the two nappes of the cone in hyperbola, resulting in the development of two discontinuous open curves.
Conic sections can be interpreted as a natural model of the geometry of perspective where the scene being viewed consists of circles, or more commonly, an ellipse, in addition to offering a uniform description of circles, ellipses, parabolas, and hyperbolas.
The image of the scene is often a central projection onto an image plane, with all projection rays passing through a fixed point O, the centre, and the viewer is typically a camera or the human eye. The lens plane is parallel to the image plane at the lens O.
The image of a circle c is
Eccentricity is a characteristic in conic sections that indicates how round they are. More eccentricity means less spherical behaviour, whereas less eccentricity means more spherical behaviour. It’s represented by the letter “e.”
The ratio of the distance between the focus and a point on the plane to the vertex and that point alone is the eccentricity of Hyperbola.
A parabola is a conic section formed by cutting a conical surface parallel to the side of the cone with a plane. A hyperbola is formed when a plane slices a conical surface parallel to the axis.
In mathematics, parabola and hyperbola are separate words, sections, and equations describing two different portions of a cone. These differ in shape, size, and a variety of other aspects, including the methods used to calculate them. We must first comprehend the cone and its various conic portions to comprehend them.
A hyperbola is an open curve with two branches that are mirror reflections of one another. It's made up of two curves that resemble infinite bows. The hyperbola equation, foci, eccentricity, directrix, latus rectum, and properties of such curves will all be covered here.
Students will also learn about hyperbola equations under various conditions, normal and tangents of hyperbola, vertex, focii, eccentricity, axes, and hyperbola applications, among other things. Previous year's chapter-by-chapter solutions will aid students in better understanding ideas and question patterns.
Practicing JEE past year papers would aid JEE applicants in comprehending the question pattern, marking scheme, and level of complexity of the test paper. To aid JEE applicants in their preparation, we have created chapter-by-chapter past year questions with solutions, practice papers, and more.
Students will also learn about hyperbola equations under various conditions, normal and tangents of hyperbola, vertex, focii, eccentricity, axes, and hyperbola applications, among other things. Previous year's chapter-by-chapter solutions will aid students in better understanding ideas and question patterns.