By K. R. Choubey, Chandrakant Choubey & Ravikant Choubey

Direction in arithmetic: A Lecture-wise technique is a whole source that's designed to aid scholars grasp arithmetic for the coveted IIT-JEE, AIEEE, state-level engineering front assessments and all different nation senior secondary assessments, as well as the AISSSCE. This meticulously crafted and designed sequence displays the command and authority of the authors at the topic. The sequence adopts a simple step by step method of make studying arithmetic on the senior secondary point a cheerful adventure.

Key gains:

Adopts a well-defined, meticulously deliberate and neatly dependent studying strategy. comprises lecture-wise exams that aid revise every one accomplished lecture. comprises pace Accuracy Sheets that increase the rate and accuracy of scholars and aid them revise key thoughts. offers leading edge suggestions and tips which are effortless to use and take note. contains solved Topic-Wise query Banks to reinforce the comprehension and alertness of strategies.

desk of Contents:

half A Coordinate Geometry Lecture 1 Cartesian Coordinates 1 (Introductions, distance formulation and its program, locus of some extent) Lecture 2 Cartesian Coordinates 2 (Section formulation, zone of triangle, region of quadrilateral) Lecture 2 Cartesian Coordinates 2 (Slope of a line, detailed issues in triangle (centroid, circumcentre centroid, orthocenter, incentre and excentre ) half B immediately Line Lecture 1 instantly strains 1 (Some vital effects attached with one immediately line, point-slope shape, symmetric shape or distance shape, issues shape, intercept shape equation of the directly traces) Lecture 2 directly traces 2 (Normal shape equation of the instantly line, the overall shape equation of the instantly line, aid of the overall shape into diversified situations, place of issues with appreciate to the immediately line ax + by way of + c and the perpendicular distance of aspect from the road ax + via + c = zero) Lecture three instantly traces three (Foot of perpendicular, mirrored image aspect or picture, a few very important effects hooked up with instantly traces, perspective among immediately traces) Lecture four directly traces four (Distance among parallel traces; place of beginning (0, zero) with appreciate to perspective among strains, angular bisectors of 2 given traces, a few small print attached with 3 directly strains) Lecture five immediately traces five (Miscellaneous questions, revision of hetero traces, a few more durable difficulties) half C Pair of heterosexual traces Lecture 1 Pair of heterosexual strains 1 (Homogeneous equations of moment measure and their a number of kinds) Lecture 2 Pair of hetero traces 2 (Some very important effects hooked up with homogenous pair of heterosexual line , common equation of moment measure) half D Circle Lecture 1 Circle 1 D.3 D.14 (Equation of circle in quite a few kinds) Lecture 2 Circle 2 D.15 D.34 (Relative place of aspect with appreciate to circle, parametric type of equation of circle, relative place of line and circle) Lecture three Circle three D.35 D.56 (Relative place of circles, pair of tangents and chord of touch draw from an enternal element) half E Conic part Lecture 1 Parabola 1 Lecture 2 Parabola 2 Lecture three Ellipse 1 Lecture four Ellipse 2 (Position of line with appreciate to an ellipse, diameter, tangents and normals, chord of content material) Lecture five Hyperbola attempt Your talents

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**Extra resources for 2D Coordinate Geometry: Course in Mathematics for the IIT-JEE and Other Engineering Entrance Examinations**

**Sample text**

Then A*, B*, C * , D* will be lines through S parallel to a*, 6*, c*, rf*, respectively. So iA*B*C*D*) = (a*Ä*c*rf*). But (^iBCZ)) = ia*b*c*d*) (by the definition of the cross ratio of four ideal points), so that (ABCD) = {A*B*C*D*). The following theorem is also true: T h e o r e m 2 . The cross ratio of four lines through a point in the first model is equal to the cross ratio (as defined in the second model) of the four corresponding ''lines'' (all passing through the corresponding ''point") in the second model.

Consider in π any square ABCD whose vertices C and D lie on d. Since A and Β do not lie on d, their images A' and 5 ' under α wiU be ordinary points of π' (Fig. 7). Suppose that Fig. 7 the diagonals AC and BD meet in K, Then Κ does not Ue on d, so that its image K' under α is an ordinary point of π'. Since C and D lie on d, their images C and D ' under α wiU be special points of Π', and, in π', A'K' is parallel to B'C\ and B'K' to A'D\ 3· Two Fundammtul Tlmorem$ on Prq/ectlye TrMnsforniMtlons Let πο be any plane through A'B' (Fig.

Abed) = ISAC] [SXD] ISCB^'lSDBy The triangles SAC and SC Β have the same height. If they have the same orientation, then the ratio [SAC]: [SCB] is posi tive and equal to the ratio of the bases of the triangles: ISAC] AC AC since in this case the vectors and CB have the same direction. If the triangles have opposite orientation, the ratio of their oriented areas is negative, and its absolute value is the ratio of their bases: [SAC] AC AC [5Cß] " " C 5 since the vetcors AC and CB have opposite directions.