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## Revision Notes for Class 11 Mathematics Chapter 11 Conic Sections

Class 11 Mathematics students should refer to the following concepts and notes for Chapter 11 Conic Sections in Class 11. These exam notes for Class 11 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks

### Chapter 11 Conic Sections Notes Class 11 Mathematics

**Key Concepts**

1. Let l be a fixed vertical line and m be another line intersecting it at a fixed point V and inclined to it at and angle a

On rotating the line m around the line l in such a way that the angle a remains constant a surface is generated is a double-napped right circular hollow cone.

2. The point V is called the vertex; the line l is the axis of the cone. The rotating line m is called a generator of the cone. The vertex separates the cone into two parts called nappes.

3. The sections obtained by cutting a double napped cone with a plane are called conic sections. Conic sections are of two types (i) degenerate conics (ii) non degenerate conics.

4. If the cone is cut at its vertex by the plane then degenerate conics are obtained.

5. If the cone is cut at the nappes by the plane then non degenerate conics are obtained.

6. Degenerate conics are point, line and double lines.

7. Circle, parabola, ellipse and hyperbola are degenerate conics.

8. When the plane cuts the nappes (other than the vertex) of the cone,degenerate conics are obtained.

(a) When β = 90o , the section is a circle.

The plane cuts the cone horizontally.

(b) When α < β < 90o, the section is an ellipse.

The plane cuts one part of the cone in an inclined manner

(c) When β = α; the section is a parabola.

The plane cuts the cone in such a way that it is parallel to a generator

(d) When 0 ≤ β < α; the plane cuts through both the nappes the curve of intersection is a hyperbola.

The plane cuts both parts of the cone.

9. When the plane cuts at the vertex of the cone, we have the following different cases:

(a) When α <β ≤ 90^{0}, then the section is a point.

(b) When β = α, the plane contains a generator of the cone and the section is a straight line.

It is the degenerated case of parabola.

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#### CBSE Class 11 Mathematics Chapter 11 Conic Sections Notes

We hope you liked the above notes for topic Chapter 11 Conic Sections which has been designed as per the latest syllabus for Class 11 Mathematics released by CBSE. Students of Class 11 should download and practice the above notes for Class 11 Mathematics regularly. All revision notes have been designed for Mathematics by referring to the most important topics which the students should learn to get better marks in examinations. Our team of expert teachers have referred to the NCERT book for Class 11 Mathematics to design the Mathematics Class 11 notes. After reading the notes which have been developed as per the latest books also refer to the NCERT solutions for Class 11 Mathematics provided by our teachers. We have also provided a lot of MCQ questions for Class 11 Mathematics in the notes so that you can learn the concepts and also solve questions relating to the topics. We have also provided a lot of Worksheets for Class 11 Mathematics which you can use to further make yourself stronger in Mathematics.

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