# Analytical Geometry Study Materials 2020 – Download B.Sc Study Notes PDF & Imp Questions

## 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 PDF Download Other Study Materials Click Here

## Chapters & Topics

Conics

• 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
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Conicoids

• Paraboloids
• 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 :

• IGNOU
• 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

### Important Questions

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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