# 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 y2= 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)

## Lecture - 7

• NCERT Miscellaneous Exercise (Q4 to Q8)