- Books Name
- AMARENDRA PATTANAYAK Mathmatics Book

- Publication
- KRISHNA PUBLICATIONS

- Course
- CBSE Class 11

- Subject
- Mathmatics

**Chapter 11**

**Conic Sections**

**Sections of a cone: circle, parabola, hyperbola, ellipse:**

When the plane cuts the nappe (other than the vertex) of the cone, we have the following situations:

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

**(b)**** **When a < b < 90o, the section is an *ellipse** *.

**(c)**** **When b = a; the section is a *parabola** *.

(In each of the above three situations, the plane cuts entirely across one nappe of the cone).

**(d)**** **When 0 £ b < a; the plane cuts through both the nappes and the curves of intersection is a *hyperbola** *.

**Circle: **Set of points in a plane equidistant from a fixed point. A circle with radius r and centre (h, k) can be represented as (x – h)^{2 }+ (y – k)^{2 }= r^{2}

**Parabola:** Set of points in a plane that are equidistant from a fixed-line and point. A parabola with a > 0, focus at (a, 0), and directrix x = – a can be represented as y^{2 }= 4ax

In parabola y^{2 }= 4ax, the length of the latus rectum is given by 4a.

**Ellipse: **The sum of distances of a set of points in a plane from two fixed points is constant. An ellipse with foci on the x-axis can be represented as:

**Hyperbola: **The difference of distances of set of points in a plane from two fixed points is constant. The hyperbola with foci on the x-axis can be represented as: