**CONTENT**

1. Introduction

2. Coordinates, Lengths of Straight Lines and Areas of

Triangles

Polar coordinates

3. Locus, Equation to a Locus

4. The Straight Line, Rectangular Coordinates

Straight line through two points

Angle between two given straight lines

Conditions that they may be parallel and perpendicular

Length of a perpendicular

Bisectors of angles

5. The Straight Line (Continued)

Polar Equations and Oblique Coordinates

Equations involving an arbitrary constant

Examples of loci

6. On Equations Representing Two or More Straight Lines

Angle between two lines given by one equation

General equation of the second degree

7. Transformation of Coordinates

Invariants

8. The Circle

Equation to a tangent

Pole and polar

Equation to a circle in polar coordinates

Equation referred to oblique axes

Equations in terms of one variable

9. Systems of Circles

Orthogonal circles

Radical axis

Coaxal circles

10. The Parabola

Equation to a tangent

Some properties of the parabola

Pole and polar

Diameters

Equations in terms of one variable

11. The Parabola (Continued)

Loci connected with the parabola

Three normals passing through a given point

Parabola referred to two tangents as axes

12. The Ellipse

Auxiliary circle and eccentric angle

Equation to a tangent

Some properties of the ellipse

Pole and polar

Conjugate diameters

Four normals through any point

Examples of loci

13. The Hyperbola

Asymptotes

Equation referred to the asymptotes as axes

One variable. Examples

14. Polar Equation of a Conic Section, Its Focus being the Pole

Polar equation to a tangent, polar, and normal

15. General Equation of the Second Degree, Tracing of Curves

Particular cases of conic sections

Transformation of equation to centre as origin

Equation to asymptotes

Tracing a parabola

Tracing a central conic

Eccentricity and foci of general conic

16. The General Conic

Tangent

Conjugate diameters

Conics through the intersections of two conics

The equation S = uv

General equation to the pair of tangents drawn from

any point

The director circle

The foci

The axes

Lengths of straight lines drawn in given directions

to meet the conic.

Conics passing through four points

Conics touching four lines

The conic LM = R2

17. Miscellaneous Propositions

On the four normals from any point to a central conic

Confocal conics

Circles of curvature and contact of the third order

Envelopes

Answers