Understand the transformation of axes in two dimensions. 🔄
Learn the joint equation of a pair of straight lines and angle between them. 📏
Explore circles, tangents, normals, and chords of contact. 🔵
Understand the general equation of a conic. ✨
Study special properties of parabola, ellipse, and hyperbola. 🌟
📝 Instructions
🧑🏫 For the Paper-Setter
The question paper will consist of three sections: A, B, and C.
Sections A and B will have four questions each from their respective syllabus sections.
Section C will contain one compulsory question with eleven short answer-type questions covering the entire syllabus uniformly.
Sections A and B: Each question will carry 10 marks.
Section C: This section will carry a total of 11 marks. ✍️
🎓 For the Candidates
Candidates are required to attempt five questions in total.
Select two questions from each of Sections A and B.
Additionally, candidates must answer the compulsory question from Section C. 🖋️
📘 Syllabus
Section A 🔢
Transformation of Axes:
Transformation of axes in two dimensions, shifting of origin, rotation of axes, and invariants. 🔄
Pair of Straight Lines:
Joint equation of a pair of straight lines and angle between them.
Conditions of parallelism and perpendicularity.
Joint equation of angle bisectors and lines joining the origin to the intersection of a line and a curve. 📏
Circle:
General equation of a circle. Circle through the intersection of two lines, tangents, normals, chord of contact, pole and polar.
Pair of tangents from a point, equation of chord in terms of mid-point, angle of intersection, orthogonality, power of a point.
Radical axis, coaxial family of circles, and limiting points. 🔵
Section B 🌟
General Equation of a Conic:
Equation and properties of general conic sections, tangents, normals, chord of contact, pole and polar, pair of tangents from a point, and equation of a chord in terms of the mid-point. ✨
Special Properties:
Detailed study of parabola, ellipse, and hyperbola with their properties and applications.
Conjugate hyperbola, asymptotes of hyperbola, rectangular hyperbola.
Conjugate diameters of ellipse and hyperbola.
Identification of conic in general second-degree equations. 🌌
📚 Books Recommended
S.L. Loney: 'The Elements of Coordinate Geometry', Macmillan and Company, London (2nd Edition, 2007). 📘
P.K. Jain and Khalil Ahmad: 'A Textbook of Analytical Geometry of Two Dimensions', Wiley Eastern Ltd. (1999). 📚
Erwin Kreyszig: 'Advanced Engineering Mathematics', John Wiley & Sons. 📖
Gorakh Prasad and H.C. Gupta: 'Textbook on Coordinate Geometry', Pothishala Pvt. Ltd., Allahabad (1955). 🔢