# The Elements of Coordinate Geometry Cartesian Coordinates Part - 1 (English) 4th Edition

• ISBN: 9789351414940
• Authors: S L Loney
INR 95/-
INR 124/-

## The Elements of Coordinate Geometry Cartesian Coordinates Part - 1 (English) 4th Edition

Author: S L Loney
Language: English
Length (Pages): 403 Pages
Publisher: Arihant

Publication Year 2014 March
Edition:4th
Exam:
ISBN: 9789351414940

1. Introduction - Some Algebraic Results
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 - Polar Equations and Oblique Coordinates
Equations Involving an Arbitrary Constant Example of Loci
6. 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 Oblique Axes
Equation in Terms of One Variable
9. Systems of Circles
Orthogonal Circles
Coaxial Circles
10. Conic Sections - The Parabola
Equation to a Tangent
Some Properties of the Parabola
Pole and Polar
Diameters
Equation 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 to a Conic
Polar Equation to a Tangent, Polar and Normal
15. General Equation. 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. General Equation
Tangent
Conjugate Diameters
Conics through the Intersection of Two Conics
The Equation S = Luv
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