Do you know what an ‘ellipse’ is?’ Ellipse can be described as the locus or the pin of all the points in a plane structure. The points are actually placed away from each other, the sum of the distance between the points is always constant. These fixed points on the plane structure are given the name of ‘foci’ (this means singular focus), while this is surrounded by the curve. The fixed-line of the ellipse is called the directrix and the same ratio formed is known as the eccentricity of that ellipse. The meaning of ‘eccentricity’ is the factor of the ellipse which thereby demonstrates the elongation of the line.
Definition in Terms of Locus
Ellipse is the set of all the points which are on the XY- plane, the distance from the two fixed points which is known as the foci sums up to form a distinct and always constant value.
As mentioned, an ellipse is the type of conic section which is produced when the plane is cut along the cone of the angle forming the base-like structure. Now, if a cone is being dissected by the plane, forming a parallel angle with the base then that structure will form a circle.
The Shape of the Ellipse
The ellipse has an oval structure that encloses an area of the ellipse which is being defined by the major axis and the minor axis at the point. The area of the ellipse = πab. In this case, a and b represent the length of the semi-major and the semi-minor axis of the ellipse. The structure of Ellipse is the conic section like the parabola and the hyperbola which is in the open shape and unbounded in structure.
What Do You Mean by Major and Minor Axis in an Ellipse?
The structure of Ellipse is being defined by the two-axis which runs along the x and y-axis, thus the major and minor axis in ellipses is:
- Major axis
- Minor Axis
Know About Parabola
Before discussing the shape and uses of parabola, let us discuss its definition. A parabola is perfectly defined as the section of the right circular cone by the plane figure which lies parallel to the generator of the cone, this is called the parabola figure. This is the locus of a point that moves at a distance from the fixed point which is always equal to the distance that is from a fixed line, this is called the directrix.
Summing up, we know that the fixed point is called the focus while the fixed line is called the directrix.
What is the Shape of Parabola?
The shape of the parabola is in a U-shaped curve-like structure where at any point this is always at an equal distance from a single point which is called the focus. This also structures from a fixed straight line which is called the directrix.
What is the Usefulness of Parabola?
Are you yet clear about the Parabolic structure? If not, then just place an image in your head of a simply arc-like structure, that is exactly what a parabola looks like. Now, hereinafter we will discuss the parabolic equations and standard forms of definition which are used in our real life.
The satellite connection functions with the help of the parabolic disc-shapes structure. Thus, the parabola is used for the following uses:
- In fixing the radar dishes
- Helps in the satellite communication process.
- They are fixed in the satellite dishes.
- The reflector of the torches and the spotlights works with the help of a parabolic glass-like structure.
- The focus which is used to concentrate the sun rays to make a hotspot uses the parabolic structure. Visit Cuemath for further learning of these amazing concepts.