Topics
Mathematical Reasoning
- Mathematically Acceptable Statements
- New Statements from Old
- Special Words Or Phrases
- Contrapositive and Converse
- Introduction of Validating Statements
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- Difference Between Contradiction, Converse and Contrapositive
- Consolidating the Understanding
Sets
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Sets and Functions
Relations and Functions
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- Brief Review of Cartesian System of Rectanglar Co-ordinates
Algebra
Trigonometric Functions
- Concept of Angle
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Coordinate Geometry
Complex Numbers and Quadratic Equations
- Concept of Complex Numbers
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- Argand Plane and Polar Representation
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- Algebra of Complex Numbers - Equality
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- Need for Complex Numbers
- Square Root of a Complex Number
Calculus
Mathematical Reasoning
Linear Inequalities
Principle of Mathematical Induction
Statistics and Probability
Permutations and Combinations
- Fundamental Principles of Counting
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- Factorial N (N!) Permutations and Combinations
Binomial Theorem
- Introduction of Binomial Theorem
- Binomial Theorem for Positive Integral Indices
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- Rth Term from End
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Sequence and Series
Straight Lines
- Slope of a Line
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- Distance of a Point from a Line
- Brief Recall of Two Dimensional Geometry from Earlier Classes
- Shifting of Origin
- Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
Conic Sections
- Sections of a Cone
- Concept of Circle
- Introduction of Parabola
- Standard Equations of Parabola
- Latus Rectum
- Introduction of Ellipse
- Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse
- Special Cases of an Ellipse
- Eccentricity
- Standard Equations of an Ellipse
- Latus Rectum
- Introduction of Hyperbola
- Eccentricity
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- Latus Rectum
- Standard Equation of a Circle
Introduction to Three-dimensional Geometry
Limits and Derivatives
- Intuitive Idea of Derivatives
- Introduction of Limits
- Introduction to Calculus
- Algebra of Limits
- Limits of Polynomials and Rational Functions
- Limits of Trigonometric Functions
- Introduction of Derivatives
- Algebra of Derivative of Functions
- Derivative of Polynomials and Trigonometric Functions
- Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically
- Limits of Logarithmic Functions
- Limits of Exponential Functions
- Derivative of Slope of Tangent of the Curve
- Theorem for Any Positive Integer n
- Graphical Interpretation of Derivative
- Derive Derivation of x^n
Statistics
- Measures of Dispersion
- Concept of Range
- Mean Deviation
- Introduction of Variance and Standard Deviation
- Standard Deviation
- Standard Deviation of a Discrete Frequency Distribution
- Standard Deviation of a Continuous Frequency Distribution
- Shortcut Method to Find Variance and Standard Deviation
- Introduction of Analysis of Frequency Distributions
- Comparison of Two Frequency Distributions with Same Mean
- Statistics Concept
- Central Tendency - Mean
- Central Tendency - Median
- Concept of Mode
- Measures of Dispersion - Quartile Deviation
- Standard Deviation - by Short Cut Method
Probability
- Random Experiments
- Introduction of Event
- Occurrence of an Event
- Types of Events
- Algebra of Events
- Exhaustive Events
- Mutually Exclusive Events
- Axiomatic Approach to Probability
- Probability of 'Not', 'And' and 'Or' Events
Definition
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 in following fig.
To find the Length of the latus rectum of the parabola `y^2` = 4ax in following fig.
By the definition of the parabola, AF = AC.
But AC = FM = 2a
Hence AF = 2a.
And since the parabola is symmetric with respect to x-axis AF = FB and so
AB = Length of the latus rectum = 4a.
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