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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

  1. The distance between the points (0, 0) and (3, 4) is:

    • 5
    • 7
    • 12
    • 25
    Show answer

    Answer: 5

  2. The slope of the line y = 2x + 3 is:

    • 2
    • 3
    • −2
    • 1/2
    Show answer

    Answer: 2

  3. The equation of a circle with centre at the origin and radius r is:

    • x² + y² = r²
    • x² − y² = r²
    • x + y = r
    • x² + y² = 2r
    Show answer

    Answer: x² + y² = r²

  4. For two perpendicular lines, the product of their slopes is:

    • 1
    • −1
    • 0
    • Undefined
    Show answer

    Answer: −1

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Practice Questions

Practise randomly selected JEE questions on Coordinate Geometry. Answers are revealed after each question.

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