Parabola in Maths
What is Parabola?
Parabola is the set of all points that are equidistant from a fixed point (called the focus) and a fixed straight line (called the directrix).
What is meant by Conjugate Axis of a Parabola?
A line that passes through the vertex of the parabola and is perpendicular to its transverse axis is called the conjugate axis of the parabola.
What are Applications of Parabola?
Parabolas are used for a variety of purposes some of them are
- Parabolic arch is used in the construction of various monuments.
- Parabolic mirrors are used in reflecting telescopes, satellites, etc.
- Parabolas are used in various mathematical calculations, such as tracing the path of a missile, the trajectory of a bullet, etc.
What is Shape of a Parabola?
Graph of a parabola is in the shape of U.
What is Eccentricity of a Parabola?
Eccentricity is defined as the ratio of distances of any point of conic section to its focus and corresponding directrix. For parabola eccentricity is 1.
What is Formula for Length of Latus Rectum of a Parabola?
For parabola y2 = 4ax, length of the latus rectum is calculated by 4a..
What is Vertex of a Parabola?
Point of intersection of the parabola and both the conjugate axis is called the vertex of a parabola. If the equation of parabola is y2 = 4ax, then the vertex is (0, 0).
What is a Parabolic motion?
Parabola motion, also known as projectile motion, describes the path followed by an object that is subject only to the force of gravity and no other external forces, such as air resistance. In this type of motion, the object moves in a curved path that resembles a parabola.
What are 4 Types of Parabola?
Parabolas can generally be categorized into four types based on their orientation and direction:
- Vertical Opening Up: Standard form is y = ax2 + bx + c, where a > 0.
- Vertical Opening Down: Standard form is y = ax2+ bx + c, where a < 0.
- Horizontal Opening Right: Standard form is x = ay2+ by + c, where a > 0.
- Horizontal Opening Left: Standard form is x = ay2+ by + c, where a < 0.
What is difference between Parabola and Hyperbola?
Parabola is a U-shaped curve where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix). It has one axis of symmetry.
Hyperbola is a curve where the difference of the distances from two points (the foci) is constant. It has two disconnected parts and two axes of symmetry.
What are 4 key Features of a Parabola?
- Vertex: Highest or lowest point of the parabola.
- Axis of Symmetry: Line that divides the parabola into two symmetric halves.
- Focus: A fixed point through which all the parallel light rays reflect off a parabolic mirror.
- Directrix: A fixed line that is equidistant from all points on the parabola.
Who invented Parabola?
Concept of the parabola and its mathematical properties have been studied and developed over centuries by various mathematicians and scholars. However, it was the ancient Greek mathematician Apollonius of Perga who extensively studied conic sections, including the parabola, around the 3rd century BCE.
Parabola – Graph, Properties, Examples & Equation of Parabola
Parabola is one of the conic sections in Math. It is an intersection of a surface plane and a double-napped cone. A parabola is a U-shaped curve that can be either concave up or down, depending on the equation. Parabolic curves are widely used in many fields such as physics, engineering, finance, and computer sciences.
In this article, we will understand What a Parabola is, its Graph, Parabola Properties, Parabola Examples, Parabola Equation, and others in detail.
Table of Content
- What is Parabola in Maths?
- Parabola Shape
- Parabola Equation
- Properties of Parabola
- Graph of Parabola
- Parametric Coordinates of a Parabola
- Equation of Tangent to a Parabola
- Director Circle of Parabola
- Equation of Normal to a Parabola
- Equation of Normal in Slope Form
- Equation of Normal in Point Form
- Equation of Normal in Parametric Form