Greetings to all, Today we are going to upload the Conic Sections Class 11 Formulas PDF to assist students as well tutors. Conic Sections Class 11 Formulas & Notes is prepared rigidly as per the NCERT Syllabus which not only decreases the pressure on the students but also, offers them an easy way to study or revise the chapter. These formulae are cumulated from the past 15 years of study material selected by CBSE so that no significant formulae should be left-back for the students to know and practice.
Conic Sections Class 11 Formulas & Notes would boost your exam practice and increase your self-confidence which would assist you to score maximum marks in the exam.
Detailed Table of Chapter 11 Notes – Conic Sections Class 11 Formulas PDF
| 1. | Board | CBSE |
| 2. | Textbook | NCERT |
| 3. | Class | Class 11 |
| 4. | Subject | Notes |
| 5. | Chapter | Chapter 11 |
| 6. | Chapter Name | Conic Sections |
| 7. | Category | CBSE Revision Notes |
Conic Sections Class 11 Formulas PDF- All formulae
Circle
A circle is the set of all points in a plane, which are at a fixed distance from a fixed point in the plane. The fixed point is called the center of the circle and the distance from the center to any point on the circle is called the radius of the circle.
The equation of a circle with radius r having a center (h, k) is given by (x – h)2 + (y – k)2 = r2.
The general equation of the circle is given by x2 + y2 + 2gx + 2fy + c = 0 , where, g, f and c are constants.
- The center of the circle is (-g, -f).
- The radius of the circle is r = g2+f2−c−−−−−−−−−√
The general equation of the circle passing through origin is x2 + y2 + 2gx + 2fy = 0.
The parametric equation of the circle x2 + y2 = r2 are given by x = r cos θ, y = r sin θ, where θ is the parametre and the parametric equation of the circle (x – h)2 + (y – k)2 = r2 are given by x = h + r cos θ, y = k + r sin θ.
Note: The general equation of the circle involves three constants which implies that at least three conditions are required to determine a circle uniquely.
Parabola
A parabola is the set of points P whose distances from a fixed point F in the plane are equal to their distance from a fixed-line l in the plane. The fixed point F is called focus and the fixed-line l is the directrix of the parabola.
Main Facts About the Parabola
| Forms of parabola | y2= 4ax | y2 = -4ax | x2 = 4ay | x2 = -4ay |
| Axis of parabola | y = 0 | y = 0 | x = 0 | x = 0 |
| Directrix of parabola | x = -a | x = a | y = -a | y = a |
| Vertex | (0, 0) | (0, 0) | (0, 0) | (0, 0) |
| Focus | (a, 0) | (-a, 0) | (0, a) | (0, -a) |
| Length of latus rectum | 4a | 4a | 4a | 4a |
| Focal length | |x + a| | |x – a| | |y + a| | |y – a| |
Ellipse
An ellipse is the set of all points in a plane such that the sum of whose distances from two fixed points is constant.
or
An ellipse is the set of all points in the plane whose distances from a fixed point in the plane bears a constant ratio, less than their distance from a fixed point in the plane. The fixed point is called focus, the fixed-line a directrix, and the constant ratio(e) the eccentricity of the ellipse. We have two standard forms of ellipse i.e.
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