Topics
Angle and Its Measurement
- Directed Angle
- Angles of Different Measurements
- Angles in Standard Position
- Measures of Angles with Various Systems
- Area of a Sector
- Length of an Arc
Trigonometry - 1
- Trigonometric Ratios
- Trigonometric Functions with the Help of a Circle
- Signs of Trigonometric Functions in Different Quadrants
- Range of Cosθ and Sinθ
- Trigonometric Functions of Specific Angles
- Trigonometric Functions of Negative Angles
- Important Identities and Standard Results
- Periodicity of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Graphs of Trigonometric Functions
- Polar Co-ordinate System
Trigonometry - 2
Determinants and Matrices
- Expansion of Determinant
- Minors and Cofactors of Elements of Determinants
- Properties of Determinants
- Application of Determinants
- Determinant Method (Cramer’s Rule)
- Consistency of Three Equations in Two Variables
- Area of Triangle and Collinearity of Three Points
- Concept of Matrices
- Types of Matrices
- Operations on Matrices>Scalar Multiplication
- Operations on Matrices> Matrix Multiplication
- Transpose of a Matrix
Straight Line
- Locus of a Points in a Co-ordinate Plane
- Equations of Line in Different Forms
- Family & Concurrent Lines
Circle
Conic Sections
Measures of Dispersion
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
Probability
Complex Numbers
Sequences and Series
- Sequence, Series, and Progression
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Harmonic Progression (H. P.)
- Arithmetico Geometric Series
- Power Series
Permutations and Combination
Methods of Induction and Binomial Theorem
- Principle of Mathematical Induction
- Binomial Theorem for Positive Integral Index
- General Term in Expansion of (a + b)n
- Middle term(s) in the expansion of (a + b)n
- Binomial Theorem for Negative Index Or Fraction
- Binomial Coefficients
Sets and Relations
- Sets and Their Representations
- Classification of Sets
- Basics of Relations & Functions
- Intervals
Functions
Limits
Continuity
Differentiation
- Concept of Differentiability
- Rules of Differentiation (Without Proof)
- Derivative of Algebraic Functions
- Derivative of Inverse Function
- Exponential and Logarithmic Functions
- Exponential and Logarithmic Functions
- L' Hospital'S Theorem
Estimated time: 4 minutes
Maharashtra State Board: Class 12
Definition: Parabola
A parabola is the locus of a point which moves in a plane such that its distance from a fixed point (i.e. focus) is always equal to its distance from a fixed straight line (i.e. directrix).
Maharashtra State Board: Class 12
Key Points: Parabola
| Property | y² = 4ax | y² = −4ax | x² = 4ay | x² = −4ay |
|---|---|---|---|---|
| Vertex | (0, 0) | (0, 0) | (0, 0) | (0, 0) |
| Focus | (a, 0) | (−a, 0) | (0, a) | (0, −a) |
| Directrix | x + a = 0 | x − a = 0 | y + a = 0 | y − a = 0 |
| Axis | y = 0 | y = 0 | x = 0 | x = 0 |
| Axis of Symmetry | X-axis | X-axis | Y-axis | Y-axis |
| Eccentricity | 1 | 1 | 1 | 1 |
| Latus Rectum Length | 4a | 4a | 4a | 4a |
| Endpoints of Latus Rectum | (a, ±2a) | (−a, ±2a) | (±2a, a) | (±2a, −a) |
| Equation of Latus Rectum | x = a | x = −a | y = a | y = −a |
| Tangent at Vertex | x = 0 | x = 0 | y = 0 | y = 0 |
| Parametric Equations | x = at², y = 2at | x = −at², y = 2at | x = 2at, y = at² | x = 2at, y = −at² |
| Parametric Point | (at², 2at) | (−at², 2at) | (2at, at²) | (2at, −at²) |
| Focal Distance of P(x₁,y₁) | x₁ + a | a − x₁ | y₁ + a | a − y₁ |
Shaalaa.com | Standard equation of parabola
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