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Analytical Geometry, 1/e : 2D and 3D
- Author / Creator
- Available as
- Online
- Summary
-
PMP® Certification: Excel with Ease is a self-study guide and is essential to all PMP aspirants to clear the certification exam in the first attempt itself. The book is based on A Guide to the Proj...
PMP® Certification: Excel with Ease is a self-study guide and is essential to all PMP aspirants to clear the certification exam in the first attempt itself. The book is based on A Guide to the Project Management Body of Knowledge (PMBOK® Guide), fifth edition, which presents a set of standard terminology and guidelines for project management. The content presented in an easy to understand format which shall help students to grasp concepts quickly.
Details
- Format
- Books
- Language
- English
- Publication
-
- 1st ed
- Delhi : Pearson India, 2013
- ©2013
- Physical Details
-
- 1 online resource (753 pages)
- ISBNs
- 9789332517639, 9332517630, 129995491X
- OCLC
- on1024243802, on1432178024
- Includes index.
- Cover -- Dedication -- Brief Contents -- Contents -- About the Author -- Preface -- Chapter 1: Coordinate Geometry -- 1.1 Introduction -- 1.1.1 Distance between Two Given Points -- 1.2 Section Formula -- 1.2.1 Coordinates of the Point that Divides the Line Joining Two Given Points in a Given Ratio -- 1.2.2 External Point of Division -- 1.2.3 Centroid of a Triangle Given its Vertices -- 1.2.4 Area of Triangle ABC with Vertices A(x1, y1), B(x2, y2) and C(x3, y3) -- 1.2.5 Area of the Quadrilateral Given its Vertices -- Illustrative Examples -- Exercises -- Chapter 2: The Straight Line -- 2.1 Introduction -- 2.1.1 Determination of the General Equation of a Straight Line -- 2.1.2 Equation of a Straight Line Parallel to y-axis and at a Distance of h units from x-axis -- 2.2 Slope of a Straight Line -- 2.3 Slope-intercept Form of a Straight Line -- 2.4 Intercept Form -- 2.5 Slope-point Form -- 2.6 Two Points Form -- 2.7 Normal Form -- 2.8 Parametric Form and Distance Form -- 2.9 Perpendicular Distance on a Straight Line -- 2.10 Intersection of Two Straight Lines -- 2.11 Concurrent Straight Lines -- 2.12 Angle between Two Straight Lines -- 2.13 Equations of Bisectors of the Angle between Two Lines -- Illustrative Examples -- Exercises -- Chapter 3: Pair of Straight Lines -- 3.1 Introduction -- 3.2 Homogeneous Equation of Second Degree in x and y -- 3.3 Angle between the Lines Represented by ax 2 + 2hxy + by 2 = 0 -- 3.4 Equation for the Bisector of the Angles between the Lines Given by ax2 + 2hxy + by2 = 0 -- 3.5 Condition for General Equation of a Second Degree Equation to Represent a Pair of Straight Lines -- Illustrative Examples -- Exercises -- Chapter 4: Circle -- 4.1 Introduction -- 4.2 Equation of a Circle whose Centre is (h, k) and Radius r -- 4.3 Centre and Radius of a Circle Represented by the Equation x2 + y2 + 2gx + 2fy + c = 0
- 4.4 Length of Tangent from Point P(x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0 -- 4.5 Equation of Tangent at (x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0 -- 4.6 Equation of Circle with the Line Joining Points A (x1, y1) and B (x2, y2) as the ends of Diameter -- 4.7 Condition for the Straight Line y = mx + c to be a Tangent to the Circle x2 + y2 = a2 -- 4.8 Equation of the Chord of Contact of Tangents from (x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0 -- 4.9 Two Tangents Can Always Be Drawn from a Given Point to a Circle and the Locus of the Point of Intersection of Perpendicular Tangents is a Circle -- 4.10 Pole and Polar -- 4.10.1 Polar of the Point P (x1, y1) with Respect to the Circle x2 + y2 + 2gx + 2fy + c = 0 -- 4.10.2 Pole of the Line lx + my + n = 0 with Respect to the Circle x2 + y2 = a2 -- 4.11 Conjugate Lines -- 4.11.1 Condition for the Lines lx + my + n = 0 and l1x + m1y + n1 = 0 to be Conjugate Lines with Respect to the Circle x2 + y2 = a2 -- 4.12 Equation of a Chord of Circle x2 + y2 + 2gx + 2fy + c = 0 in Terms of its Middle Point -- 4.13 Combined Equation of a Pair of Tangents from (x1, y1) to the Circle x2 + y2 + 2gx + 2fy + c = 0 -- 4.14 Parametric Form of a Circle -- 4.14.1 Equation of the Chord Joining the Points 'θ' and 'ᵩ' on the Circle and the Equation of the Tangent at θ -- Illustrative Examples -- Exercises -- Chapter 5: System of Circles -- 5.1 Radical Axis of Two Circles -- 5.2 Orthogonal Circles -- 5.3 Coaxal System -- 5.4 Limiting Points -- 5.5 Examples (Radical Axis) -- 5.6 Examples (Limiting Points) -- Exercises -- Chapter 6: Parabola -- 6.1 Introduction -- 6.2 General Equation of a Conic -- 6.3 Equation of a Parabola -- 6.4 Length of Latus Rectum -- 6.4.1 Tracing of the curve y2 = 4ax -- 6.5 Different Forms of Parabola -- Illustrative Examples Based on Focus Directrix Property
- 6.6 Condition for Tangency -- 6.7 Number of Tangents -- 6.8 Perpendicular Tangents -- 6.9 Equation of Tangent -- 6.10 Equation of Normal -- 6.11 Equation of Chord of Contact -- 6.12 Polar of a Point -- 6.13 Conjugate Lines -- 6.14 Pair of Tangents -- 6.15 Chord Interms of Mid-point -- 6.16 Parametric Representation -- 6.17 Chord Joining Two Points -- 6.18 Equations of Tangent and Normal -- 6.19 Point of Intersection of Tangents -- 6.20 Point of Intersection of Normals -- 6.21 Number of Normals from a Point -- 6.22 Intersection of a Parabola and a Circle -- Illustrative Examples Based on Tangents and Normals -- Illustrative Examples Based on Parameters -- Exercises -- Chapter 7: Ellipse -- 7.1 Standard Equation -- 7.2 Standard Equation of an Ellipse -- 7.3 Focal Distance -- 7.4 Position of a Point -- 7.5 Auxiliary Circle -- Illustrative Examples Based on Focus-directrix Property -- 7.6 Condition for Tangency -- 7.7 Director Circle of an Ellipse -- 7.8 Equation of the Tangent -- 7.9 Equation of Tangent and Normal -- 7.10 Equation to the Chord of Contact -- 7.11 Equation of the Polar -- 7.12 Condition for Conjugate Lines -- Illustrative Examples Based on Tangents, Normals, Pole-polar and Chord -- 7.13 Eccentric Angle -- 7.14 Equation of the Chord Joining the Points -- 7.15 Equation of Tangent at 'θ' on the Ellipse -- 7.16 Conormal Points -- 7.17 Concyclic Points -- 7.18 Equation of a Chord in Terms of Its Middle Point -- 7.19 Combined Equation of Pair of Tangents -- 7.20 Conjugate Diameters -- 7.20.1 Locus of Midpoint -- 7.20.2 Property: The Eccentric Angles of the Extremities of a Pair of Semi-conjugate Diameter Differ by a Right Angle -- 7.20.3 Property: If CP and CD are a Pair of Semi-conjugate Diameters then CD2 + CP2 is a Constant
- 7.20.4 Property: The Tangents at the Extremities of a Pair of Conjugate Diameters of an Ellipse Encloses a Parallelogram Whose Area Is Constant -- 7.20.5 Property: The Product of the Focal Distances of a Point on an Ellipse Is Equal to the Square of the Semi-diameter Which Is Conjugate to the Diameter Through the Point -- 7.20.6 Property: If PCP ' and DCD ' are Conjugate Diameter then They are also Conjugate Lines -- 7.21 Equi-conjugate Diameters -- 7.21.1 Property: Equi-conjugate Diameters of an Ellipse Lie along the Diagonals of the Rectangle Formed by the Tangent at the Ends of its Axes -- Illustrative Examples Based on Conjugate Diameters -- Exercises -- Chapter 8: Hyperbola -- 8.1 Definition -- 8.2 Standard Equation -- 8.3 Important Property of Hyperbola -- 8.4 Equation of Hyperbola in Parametric Form -- 8.5 Rectangular Hyperbola -- 8.6 Conjugate Hyperbola -- 8.7 Asymptotes -- 8.7.1 Equations of Asymptotes of the Hyperbola -- 8.7.2 Angle between the Asymptotes -- 8.8 Conjugate Diameters -- 8.9 Rectangular Hyperbola -- 8.9.1 Equation of Rectangular Hyperbola with Reference to Asymptotes as Axes -- 8.9.2 Equations of Tangent and Normal at (x1, y1) on the Rectangular Hyperbola xy = c2 -- 8.9.3 Equation of Tangent and Normal at (ct,c/t)on the Rectangular Hyperbola xy = c2 -- 8.9.4 Equation of the Chord Joining the Points 't1' and 't2' on the Rectangular Hyperbola xy = c2 and the Equation of the Tangent at t -- 8.9.5 Properties -- 8.9.6 Results Concerning the Rectangular Hyperbola -- 8.9.7 Conormal Points-Four Normal from a Point to a Rectangular Hyperbola -- 8.9.8 Concyclic Points on the Rectangular Hyperbola -- Exercises -- Chapter 9: Polar Coordinates -- 9.1 Introduction -- 9.2 Definition of Polar Coordinates -- 9.3 Relation between Cartesian Coordinates and Polar Coordinates -- 9.4 Polar Equation of a Straight Line
- 9.5 Polar Equation of a Straight Line in Normal Form -- Exercises -- 9.6 Circle -- 9.6.1 Polar Equation of a Circle -- 9.6.2 Equation of the Chord of the Circle r = 2a cos θ on the Line Joining the Points (r1, θ1) and (r2, θ2). -- 9.6.3 Equation of the Normal at α on the Circle r = 2cosθ -- 9.6.4 Equation of the Circle on the Line Joining the Points (a, α) and (b, β) as the Ends of a Diameter -- 9.7 Polar Equation of a Conic -- 9.7.1 Polar Equation of a Conic -- 9.7.2 Equation to the Directrix Corresponding to the Pole -- 9.7.3 Equation to the Directrix Corresponding to Focus Other than the Pole -- 9.7.4 Equation of Chord Joining the Points whose Vectorial Angles are ` - a and ` + a on the Conic -- 9.7.5 Tangent at the Point whose Vectorial Angle is ` on the Coniclr=1+ ecosp -- 9.7.6 Equation of Normal at the Point whose Vectorial Angle is a on the Conic -- 9.7.7 Asymptotes of the Conic islr=1+ecosp (e>1) -- 9.7.8 Equation of Chord of Contact of Tangents from (r1,p1) to the Conic -- 9.7.9 Equation of the Polar of any Point (r1,p1) with Respect to the Coniclr=1+ ecosp -- Exercises -- Chapter 10: Tracing of Curves -- 10.1 General Equation of the Second Degree and Tracing of a Conic -- 10.2 Shift of Origin Without Changing the Direction of Axes -- 10.3 Rotation of Axes Without Changing the Origin -- 10.4 Removal of XY-term -- 10.5 Invariants -- 10.6 Conditions for the General Equation of the Second Degree to Represent a Conic -- 10.7 Centre of the Conic Given by the General Equation of the Second Degree -- 10.8 Equation of the Conic Referred to the Centre as Origin -- 10.9 Length and Position of the Axes of the Central Conic whose Equation is ax2 + 2hxy + by2 = 1 -- 10.10 Axis and Vertex of the Parabola whose Equation is ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 -- Exercises -- Chapter 11: Three Dimension -- 11.1 Rectangular Coordinate Axes
- 11.2 Formula for Distance between Two Points