Ellipse x²/a² + y²/b² = 1: foci, axes, PF₁ + PF₂ = 2aदीर्घवृत्त x²/a² + y²/b² = 1: नाभियाँ, अक्ष, PF₁ + PF₂ = 2aEllipse x²/a² + y²/b² = 1: foci, axes, PF₁ + PF₂ = 2a

Section 10.5 · Class 11 Maths Ch 10 · interactive diagram

Parts and what they mean

• Ellipse (दीर्घवृत्त) — Points whose distances from two fixed points (foci) add up to a constant.
• Foci F₁, F₂ (नाभियाँ F₁, F₂) — (±c, 0) with c² = a² − b²; here c = 4. Eccentricity e = c/a = 4/5 (< 1).
• Vertices (शीर्ष) — Ends of the major axis: (±a, 0) = (±5, 0).
• Major axis 2a (दीर्घ अक्ष 2a) — Through the foci; length 2a = 10.
• Minor axis 2b (लघु अक्ष 2b) — Perpendicular to the major axis at the centre; length 2b = 6.
• Point P (बिंदु P) — PF₁ + PF₂ = 2a = 10 for every point on the ellipse.
• Standard equation (मानक समीकरण) — x²/a² + y²/b² = 1 (a > b), c² = a² − b², latus rectum 2b²/a. If the larger number is under y², the major axis is the y-axis.

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