Download Analytical Geometry Study Materials 2020. In this article, we are going to provide Study Notes for the School of Sciences. This subject is very important for B.Sc (Mathematics). This subject covers the topics of Conics, Sphere, Cylinder, Cone, Conicoids, etc. Through this article, you can download Unit wise PDFs, Chapters, Topics, and Important Questions. Read the below article, to download the material PDFs.
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Table of Contents
Analytical Geometry Study Materials
|Name of the Subject||Analytical Geometry|
|Category||School of Sciences|
|Useful for||Bachelor of Science|
|Course Type||Under Graduation Courses|
|Article on||Study Materials 2020|
|Study Material Format|
|Download Other Study Materials||Click Here|
Analytical Geometry Study Books
Chapters & Topics
- General Theory of Conics
- The Standard Conics
- Preliminaries in Plane Geometry
The Sphere, Cone and Cylinder
- Cones and Cylinders
- The Sphere
- Preliminaries in Three-Dimensional Geometry
- Central Conicoids
- General Theory of Conicoids
Subject in the Universities
This subject will be useful to the students who are pursuing a Bachelor of Science. The following university students can also download Analytical Geometry study materials :
- Uttarakhand Open University
- University of Calicut
- Pondicherry University
Subject in the Semesters
Analytical Geometry subject will be studied by the students in the following semesters of their respective courses :
- B.Sc Mathematics III Semester
Unit wise PDFs
Download Unit wise PDFs of Analytical Geometry subject :
|The Sphere, Cone, and Cylinder||Download|
We have mentioned some of the important questions of Analytical Geometry subject :
- Find the conic reprevented by
9x² – 24xy + 16y² – 124x + 132y + 324 = 0.
- Check whether 3×2 t 7xy + 2y2 + 5x + 5y + 2 = 0 represents a pair of lines.
- Show that the real quadratic equation ax² + 2hxy -I- by² = 0 represents a pair of lines.
- Under what conditions 011 a, b and h, will the equation in Theorem represent
- a pair of parallel lines?
- a pair of perpendicular lines?
- Identify the conic x² – 3xy + y² + lox – 10y + 21 = 0. If it is central, find its centre.
- Consider the conicoid given by the equation 2x² + 3y² + 4z² – 4x – i2y – 24z + 49 = 0. Does it have a centre? If so, find it.
- Let P(6, 3, 2), Q(5, 1, 4), R(3, -4, 7) and S(0, 2, 5) be four points in space.. Find the projection of the line segment PQ on RS.
- Find a centre of the cohicoid 14x² + 14y²+ 8z² – 4yz – 4zx – 8xy + 18x – 18y + 5 = 0. What will its
new equation be if the origin is shifted to this centre?
- Consider the hyperboloid of one sheet given by x²+y²-z²=1.
- a) What are its horizontal cross-sections for z = +- 3, +-6
- b) What are the vertical cross-sections for x = 0 or y = 0? Describe the sections in (a) and (b) geometrically.
- Do all the coordinate axes and coordinate planes intersect the surface? Give reasons for your answer.
- Show that the intersection with any plane parallel to the XY-plane of the paraboloid.
- x² + 2y² = 3z is an ellipse.
- 3x² – y² = 4x is a hyperbola.
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