“Fake It Until You Make It! Act As If You Had All The Confidence You Require Until It Becomes Your Reality.” – Brian Tracy

In this Chapter the following concepts and generalisations are studied.
A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.
The equation of a circle with center (h, k) and the radius r is $$(x – h)^2 + (y – k)^2 = r^2$$
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 equation of the parabola with focus at (a, 0) a > 0 and directrix x = – a is $$y^2 = 4ax$$
Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola.
Length of the latus rectum of the parabola y2= 4ax is 4a.
An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.
The equation of an ellipse with foci on the x-axis is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

Length of the latus rectum of the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ is $$\frac{2b^2}{a}$$
The equation of a hyperbola with foci on the x-axis is : $$\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1$$
Length of the latus rectum of the hyperbola $$\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1$$ is $$\frac{2b^2}{a}$$