# CONIC SECTIONS CLASS 11 MATHS

## Summary

*In this *Chapter* the following concepts and *generalisations* are studied.*

*A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.*

*The equation of a circle with center (h, k) and the radius r is (x - h)^2 + (y - k)^2 = r^2 *

*A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.*

*The equation of the parabola with focus at (a, 0) a > 0 and directrix x = – a is y^2 = 4ax *

*Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose *end points* lie on the parabola.*

*Length of the latus rectum of the parabola y ^{2}= 4ax is 4a.*

*An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is *a constant*.*

*The equation of an ellipse with foci on the x-axis is \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 *

*Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose *end points* lie on the ellipse.*

*Length of the latus rectum of the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 is \frac{2b^2}{a}*

*The eccentricity of an ellipse is the ratio between the distances from the *centre* of the ellipse to one of the foci and to one of the vertices of the ellipse.*

*A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is *a constant*.*

*The equation of a hyperbola with foci on the x-axis is : \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 *

*Latus rectum of *hyperbola* is a line segment perpendicular to the transverse axis through any of the foci and whose *end points* lie on the hyperbola.*

*Length of the latus rectum of the hyperbola \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 is \frac{2b^2}{a}*

*The eccentricity of a hyperbola is the ratio of the distances from the *centre* of the hyperbola to one of the foci and to one of the vertices of the hyperbola.*

## Lecture - 1

- How to study Conic Sections in Class 11
- Introduction to Circle, Parabola, Ellipse and Hyperbola
- Animation to understand why they are called conic sections
- How to derive equation of circle
- NCERT Exercise 11.1 (Q1 to Q15)

## Lecture - 2

- Real life examples of parabola
- Standard forms of Parabola
- Definition and geometric proof for parabola
- Derivation for equation of parabola
- Way to remember all rules of parabolas
- Derivation for length of latus rectum of parabola
- NCERT Exercise 11.2 (Q1 to Q12)
- NCERT Miscellaneous Exercise (Q1 to Q3)

## Lecture - 3

- What is an ellipse with animation
- Real life examples of ellipse
- Major axis and minor axis
- Derivations for relationship between a, b and c of ellipse
- Derivation for equation of ellipse
- Derivation for latus rectum of ellipse
- Eccentricity of ellipse

## Lecture - 4

- Explanation of all basic details of standard ellipse, method to remember their rules
- NCERT Solutions Exercise 11.3 (Q1 to Q20)

## Lecture - 5

- Meaning and definition of Hyperbola
- Difference between circle, parabola, ellipse and hyperbola
- Geometrical Verification of definition of hyperbola
- Real life examples of Hyperbolas
- Transverse axis and conjugate axis of Hyperbola
- Introduction to a, b and c of hyperbolas
- Derivation for equation of standard hyperbola

## Lecture - 6

- Explanation and method to remember all rules of standard hyperbolas
- NCERT Exercise 11.4 (Q1 to Q15)