Chapter 11 Conic Sections

Mathematics Chapter 11, Grade 11 covers conic sections. It is a valuable resource that helps students achieve higher scores in both tests and various entrance exams. This article contains links to a detailed set of practice notes from Chapter 11 of the NCERT Grade 11 Math Book. This chapter requires adequate knowledge of logical thinking and analytical skills to understand basic concepts related to conic sections.

The notes prepared by Vidyakul are explained precisely and step-by-step to help students understand the right approach to solving a variety of problems. Vidyakul offers a range of learning resources to help students improve preparation and improve outcomes in the long run. Students can download the notes for Grade 11 Math Chapter 11 Conics section from this article.

MATHEMATICS NOTES CHAPTER-11

Points to Remember

• The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius is “r”. This form of the equation is helpful since you can easily find the center and the radius.

Conic Section Formulas

Check the formulas for different types of sections of a cone in the table given here.

Circle	(x−a)2+(y−b)2=r2	Center is (a,b) Radius is r
Ellipse with the horizontal major axis	(x−a)2/h2+(y−b)2/k2=1	Center is (a, b) Length of the major axis is 2h. Length of the minor axis is 2k. Distance between the centre and either focus is c with c2=h2−k2, h>k>0
Ellipse with the vertical major axis	(x−a)2/k2+(y−b)2/h2=1	Center is (a, b) Length of the major axis is 2h. Length of the minor axis is 2k. Distance between the centre and either focus is c with c2=h2−k2, h>k>0
Hyperbola with the horizontal transverse axis	(x−a)2/h2−(y−b)2/k2=1	Center is (a,b) Distance between the vertices is 2h Distance between the foci is 2k. c2=h2  + k2
Hyperbola with the vertical transverse axis	(x−a)2/k2−(y−b)2/h2=1	Center is (a,b) Distance between the vertices is 2h Distance between the foci is 2k. c2= h2  + k2
Parabola with the horizontal axis	(y−b)2=4p(x−a), p≠0	Vertex is (a,b) Focus is (a+p,b) Directrix is the line x=a−p Axis is the line y=b
Parabola with vertical axis	(x−a)2=4p(y−b), p≠0	Vertex is (a,b) Focus is (a+p,b) Directrix is the line x=b−p Axis is the line x=a

Focus, Eccentricity and Directrix of Conic

A conic section can also be described as the locus of a point P moving in the plane of a fixed point F known as focus (F) and a fixed line d known as directrix (with the focus not on d) in such a way that the ratio of the distance of point P from focus F to its distance from d is a constant e known as eccentricity. Now,

• If eccentricity, e = 0, the conic is a circle

• If 0<e<1, the conic is an ellipse

• If e=1, the conic is a parabola

• And if e>1, it is a hyperbola

So, eccentricity is a measure of the deviation of the ellipse from being circular. Suppose, the angle formed between the surface of the cone and its axis is β and the angle formed between the cutting plane and the axis is α, the eccentricity is;

e = cos α/cos β

Parameters of Conic

Apart from focus, eccentricity and directrix, there are few more parameters defined under conic sections.

• Principal Axis: Line joining the two focal points or foci of ellipse or hyperbola. Its midpoint is the centre of the curve.

• Linear Eccentricity: Distance between the focus and centre of a section.

• Latus Rectum: A chord of section parallel to directrix, which passes through a focus.

• Focal Parameter: Distance from focus to the corresponding directrix.

• Major axis: Chord joining the two vertices. It is the longest chord of an ellipse.

• Minor axis: Shortest chord of an ellipse.

Topics and Sub-topics

Students can check the complete list of topics of class 11 maths chapter 11 on Conic Sections. Before getting into the detailed notes of Conic Sections, here is a list of topics and subtopics included in this chapter:

Section Name	Topic Name
11.1	Introduction
11.2	Sections of a Cone
11.2.1	Circle, ellipse, parabola and hyperbola
11.2.2	Degenerated conic sections
11.3	Circle
11.4	Parabola
11.4.1	Standard equations of parabola
11.4.2	Latus rectum
11. 5	Ellipse
11.5.1	Relationship between semi-major axis, semi-minor axis and the distance  the focus from the centre of the ellipse
11.5.2	Special cases of an ellipse
11.5.3	Eccentricity
11.5.4	Standard equations of an ellipse
11.5.5	Latus rectum
11.6	Hyperbola
11.6.1	Eccentricity
11.6.2	Standard equation of Hyperbola
11.6.3	Latus rectum

 

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