# Conic Sections

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse. Conic section consists of those points whose distances to some point (called focus) and some line (called directrix) are in a fixed ratio, called the eccentricity. Three types of conic section are:

• Parabola
• Ellipse
• Hyperbola
• Parabola

Meaning of Parabola: Parabola is basically a curve or path followed by a ball when it got kicked. When we kick a ball, it goes up and then come down while making a U shaped curve which is called Parabola. A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane. The fixed line is called the directrix of the parabola and the fixed point F is called the focus. A line through the focus and perpendicular to the directrix is called the axis of the parabola. Standard Equation: y² = 4ax; Focus is at F (a, 0) and directrix x = -a.

Ellipse: In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location.

Length of the major axis = 2a

Length of the minor axis = 2b Standard Equation: $$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$$

Eccentricity: The eccentricity of an ellipse is the ratio between the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse.

Hyperbola:

• A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.
• The two fixed points are called the foci of the hyperbola.
• The mid-point of the line segment joining the foci is called the center of the hyperbola.
• The line through the foci is called the transverse axis and the line through the center and perpendicular to the transverse axis is called the conjugate axis.
• The points at which the hyperbola intersects the transverse axis are called the vertices of the hyperbola. Standard Equation: $$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$$

Eccentricity: The eccentricity of a hyperbola is the ratio of the distances from the centre of the hyperbola to one of the foci and to one of the vertices of the hyperbola.