“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 y^{2}= 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

Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse.

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 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.

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 equation of a hyperbola with foci on the x-axis is : \frac{x^2}{a^2} – \frac{y^2}{b^2} = 1

Latus rectum of hyperbola is a line segment perpendicular to the transverse axis through any of the foci and whose end points lie on the hyperbola.

Length of the latus rectum of the hyperbola \frac{x^2}{a^2} – \frac{y^2}{b^2} = 1 is \frac{2b^2}{a}

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