-
What is parabola and hyperbola graph?
What is parabola and hyperbola graph?
-
1 Reply
-
A parabola and a hyperbola are two different types of conic sections, which are the curves formed when a plane intersects a cone.
A parabola is a U-shaped curve that is the graph of a quadratic function, such as y = x^2 or y = -x^2. The key features of a parabola are:
It has a single point called the vertex, which is the lowest or highest point of the curve.
The curve is symmetrical about a line passing through the vertex, called the axis of symmetry.
Parabolas have applications in fields like optics, projectile motion, and architecture.
On the other hand, a hyperbola is a curve that has two separate branches that are mirror images of each other. The equation of a hyperbola is typically in the form (x/a)^2 – (y/b)^2 = 1, where a and b are constants. The key features of a hyperbola are:
It has two focal points, with the curve passing through both of them.
The curve is symmetric about two perpendicular lines called the transverse and conjugate axes.
Hyperbolas have applications in fields like astronomy, navigation, and structural engineering.
The graphs of a parabola and a hyperbola look quite different – a parabola is a single continuous curve, while a hyperbola has two separate branches. Understanding the properties of these conic sections is important in many areas of mathematics and science.
