Straight Lines
Telangana Open School (TOSS) · Class 12 · Mathematics
Complete topic list for Straight Lines in Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.
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Topics in Straight Lines
Equations of Lines Parallel to Axes
- A line parallel to the x-axis has a constant y-value and its equation is of the form $ y = b $.
- A line parallel to the y-axis has a constant x-value and its equation is of the form $ x = c $.
- If the line passes through origin, $ b = 0 $ or $ c = 0 $ respectively.
Standard Forms of Equation of a Line
- Different forms are used depending on the given information: slope-intercept, point-slope, two-point, intercept, and normal form.
- All represent the same straight line but are useful in different contexts.
- Conversion between forms is essential for problem-solving.
General Equation of a Line
- The general equation of a straight line is $ Ax + By + C = 0 $, where A and B are not both zero.
- This equation always represents a straight line.
- It can be converted into other forms for analysis.
Angle Between Two Lines
- The angle $ \theta $ between two lines with slopes $ m_1 $ and $ m_2 $ is given by $ \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| $.
- Lines are parallel if $ m_1 = m_2 $, and perpendicular if $ m_1 m_2 = -1 $.
- In general form, lines $ A_1x + B_1y + C_1 = 0 $ and $ A_2x + B_2y + C_2 = 0 $ are perpendicular if $ A_1A_2 + B_1B_2 = 0 $.
Key Concepts
Central concept: Straight Lines
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