Coordinate Geometry
Straight lines, circles, parabola, ellipse, and hyperbola
Key Concepts
- Straight lines: slope, intercept and distance formulae
- Circle: standard and general equation
- Conic sections: parabola, ellipse and hyperbola
- Eccentricity characterises each conic
- Tangents and normals to curves
Important Formulae
| Line (slope form) | y = mx + c |
| Point–line distance | |ax₀+by₀+c|/√(a²+b²) |
| Circle | (x−h)² + (y−k)² = r² |
| Parabola / ellipse | y² = 4ax; x²/a² + y²/b² = 1 |
| Eccentricity | Ellipse e = √(1−b²/a²); Hyperbola e = √(1+b²/a²) |
Quick Tips
- Two lines are perpendicular if m₁m₂ = −1, parallel if m₁ = m₂.
- Tangent to y² = 4ax: y = mx + a/m.
- For a circle, the perpendicular from the centre bisects any chord.
Sample Practice Questions
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The eccentricity of a circle is:
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Answer: 0
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The equation of a circle with centre at the origin and radius r is:
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Answer: x² + y² = r²
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For two perpendicular lines, the product of their slopes is:
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Answer: −1
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The distance between the points (0, 0) and (3, 4) is:
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Answer: 5
Practice Questions
Practise randomly selected JEE questions on Coordinate Geometry. Answers are revealed after each question.
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What are the key concepts in Coordinate Geometry for JEE?
Straight lines: slope, intercept and distance formulae; Circle: standard and general equation; Conic sections: parabola, ellipse and hyperbola; Eccentricity characterises each conic; Tangents and normals to curves.
Which formulae are important for Coordinate Geometry in JEE?
Line (slope form): y = mx + c; Point–line distance: |ax₀+by₀+c|/√(a²+b²); Circle: (x−h)² + (y−k)² = r²; Parabola / ellipse: y² = 4ax; x²/a² + y²/b² = 1; Eccentricity: Ellipse e = √(1−b²/a²); Hyperbola e = √(1+b²/a²).
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