Hyperbola x²/a² − y²/b² = 1: foci, vertices, |PF₁ − PF₂| = 2aअतिपरवलय x²/a² − y²/b² = 1: नाभियाँ, शीर्ष, |PF₁ − PF₂| = 2aHyperbola x²/a² − y²/b² = 1: foci, vertices, |PF₁ − PF₂| = 2a

Section 10.6 · Class 11 Maths Ch 10 · interactive diagram

Parts and what they mean

• Hyperbola (two branches) (अतिपरवलय (दो शाखाएँ)) — Points whose distances from two foci DIFFER by a constant.
• Foci F₁, F₂ (नाभियाँ F₁, F₂) — (±c, 0) with c² = a² + b²; here c = 5. e = c/a = 5/3 (> 1).
• Vertices (शीर्ष) — (±a, 0) = (±3, 0).
• Transverse axis 2a (अनुप्रस्थ अक्ष 2a) — Joins the vertices; length 2a = 6. Conjugate axis length 2b = 8.
• Point P (बिंदु P) — |PF₁ − PF₂| = 2a = 6 for every point on the hyperbola.
• Guide lines (asymptotes) (मार्गदर्शक रेखाएँ (अनंतस्पर्शी)) — y = ±(b/a)x — the branches get closer and closer to them. (Extra help, not in the NCERT exercises.)
• Standard equation (मानक समीकरण) — x²/a² − y²/b² = 1, c² = a² + b², latus rectum 2b²/a. The positive term tells the transverse axis.

Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 10. Report a mistake