If you want to optimize your study plan for a specific exam, let me know:
Systems of coordinates, direction cosines, and projections.
The entire foundation of 3D geometry rests on understanding Direction Cosines and Direction Ratios. Spend extra time on these introductory chapters. If your grasp on DCs and DRs is weak, you will struggle with planes and lines. Maintain a Separate Formula Sheet
If you want to tailor your study plan further, tell me you are preparing for (e.g., UPSC, CSIR NET, university exams) or which particular topic (like conicoids or skew lines) you find most challenging. I can provide targeted practice problems and conceptual shortcuts for those areas. Share public link
: Digital PDFs allow students to instantly find specific formulas, theorems, or exercise questions. analytic geometry krishna series pdf
When starting a chapter, actively write down the derivations of the formulas. Do not just read them like a novel.
| Chapter | Core Concepts | Must‑solve examples | Typical “high‑yield” practice questions | |---------|---------------|----------------------|----------------------------------------| | | Slope, intercept form, point‑slope, two‑point form, parallel & perpendicular criteria. | Ex. 3.1 – Find equation of a line passing through (2,‑3) & (‑1,4). | Q.1 – Prove two lines are perpendicular using slopes. | | 2. Pair of Straight Lines | General second‑degree equation, homogeneous part, condition for pair of lines, angle between lines. | Ex. 5.4 – Find angle between lines represented by ax²+2hxy+by²=0 . | Q.2 – Find the combined equation of lines making 30° with x‑axis. | | 3. Circles | Standard form, centre‑radius form, general equation, tangents, chord of contact, radical axis. | Ex. 7.2 – Equation of a circle passing through (1,2) and (3,‑4) with centre on x‑axis. | Q.3 – Find length of the chord intercepted by a given line. | | 4. Parabolas | Standard form ( y²=4ax , x²=4ay ), focus & directrix, latus‑rectum, parametric form, tangents, normals. | Ex. 9.5 – Find equation of tangent at parametric point t on y²=4ax . | Q.4 – Find the focus of a parabola given by x²+4xy+3y²+6x+12y+5=0 . | | 5. Ellipses & Hyperbolas | Standard forms, eccentricity, focal properties, asymptotes, parametric equations. | Ex. 12.3 – Derive equation of hyperbola with given transverse axis & asymptotes. | Q.5 – Find the length of the latus‑rectum of an ellipse 4x²+9y²=36 . | | 6. Coordinate Geometry in 3‑D (if present) | Direction ratios, dot product, line & plane equations, distance formula in space. | Ex. 14.7 – Shortest distance between a point and a line in 3‑D. | Q.6 – Find the angle between two planes. |
Analytic geometry is broadly divided into two dimensions (2D) and three dimensions (3D). The Krishna Series handles both with deep mathematical precision, typically dedicating substantial sections to the following core topics: 1. Two-Dimensional Coordinate Geometry
Analytic geometry establishes a connection between geometric shapes and algebraic equations. Unlike classical Euclidean geometry, which relies on purely visual and logical proofs without coordinates, analytic geometry uses the Cartesian coordinate system to represent points, lines, curves, and surfaces as algebraic equations. The study is generally divided into two main domains: If you want to optimize your study plan
Understanding point representation in 2D and 3D spaces.
Platforms like the Internet Archive or National Digital Library of India (NDLI) occasionally host scanned versions of older editions of standard mathematics textbooks for educational use. 3. Direct Digital Purchase
Equations of a sphere, plane section of a sphere, tangent planes, and radical planes.
Each chapter is packed with solved problems that mirror the types of questions found in university examinations. If your grasp on DCs and DRs is
I can’t help find or provide PDFs of copyrighted books. I can instead:
Comprehensive Guide to Analytic Geometry Krishna Series: Syllabus, Structure, and Study Resources
General equation, intercept form, normal form, and the angle between two planes.
Each chapter concludes with comprehensive practice problems categorized by difficulty, allowing students to test their conceptual clarity.
You can look for the physical or digital copies directly on the Krishna Prakashan website. Bookstores: Available at local educational bookstores.
for using the Krishna Series for competitive exams.