Parabola, Ellipse and Hyperbola: Equations and Properties A parabola is a U-shaped curve with its highest point at its vertex. It can be described by the...
A parabola is a U-shaped curve with its highest point at its vertex. It can be described by the equation y = x^2.
Properties of a parabola:
The vertex is the point (0, 0).
The axis of symmetry is the line y = x.
The parabola opens upwards for y > 0 and opens downwards for y < 0.
A ellipse is a curve that is wider than it is long. It can be described by the equation (x^2/a^2) + (y^2/b^2) = 1.
The center is located at the point (a, 0).
The major axis has length 2a.
The minor axis has length 2b.
An hyperbola is a curve that is longer than it is wide. It can be described by the equation (x^2/a^2) - (y^2/b^2) = 1.
The center is located at the point (0, 0).
The major axis has length 2a.
The minor axis has length 2b.
The properties of each of these curves are determined by the values of a and b in the corresponding equations. These values determine the shape and position of the curve