Conic Sections (Parabola, Ellipse, Hyperbola): One-Page Formula Sheet

Conic Sections (Parabola, Ellipse, Hyperbola) — formula sheet

Formulas

• Parabola y² = 4ax: focus (a, 0), LR = 4a, tangent y = mx + a/m
• Ellipse: b² = a²(1 − e²), LR = 2b²/a
• Hyperbola: b² = a²(e² − 1)
• Ellipse tangent condition: c² = a²m² + b²

Key ideas

• Eccentricity: parabola e = 1, ellipse e < 1, hyperbola e > 1
• Focal distance property of ellipse: PS + PS′ = 2a
• Parametric points simplify tangent and normal questions
• Condition for tangency: c² = a²m² ± b²

Traps to avoid

• Mixing ellipse and hyperbola b² relations
• Wrong focus for vertical conics
• Forgetting both tangents in slope form

jeevisionary.in/jee-topics/maths/conic-sections/