What is eccentricity and what does it tell us?

Eccentricity (e) describes the shape of a conic. e = 0 → circle; 0 1 → hyperbola. It is defined as e = c/a where c is the distance from centre to focus.

What is the latus rectum?

The latus rectum is the chord of a conic section that passes through the focus and is perpendicular to the major axis. For parabola y² = 4ax, length = 4a. For ellipse, length = 2b²/a.

How do you find the centre and radius from a general circle equation?

From x² + y² + 2gx + 2fy + c = 0, complete the square: centre = (−g, −f) and radius = √(g² + f² − c). The circle exists only when g² + f² − c > 0.

Circles, Parabolas, Ellipses and Hyperbolas

Conic Sections • Class 11 Mathematics • NCERT • CBSE

Circle: (x−h)²+(y−k)²=r². Parabola: y²=4ax (focus at (a,0)). Ellipse: x²/a²+y²/b²=1 (a>b), eccentricity e=c/a<1. Hyperbola: x²/a²−y²/b²=1, e>1.

Key Formulas

(x−h)² + (y−k)² = r² (circle)
y² = 4ax (parabola, opens right)
x²/a² + y²/b² = 1 (ellipse, a > b)
c² = a² − b² (ellipse: c = focal distance)
x²/a² − y²/b² = 1 (hyperbola)
c² = a² + b² (hyperbola)
e = c/a (eccentricity)

Frequently Asked Questions

What is eccentricity and what does it tell us?: Eccentricity (e) describes the shape of a conic. e = 0 → circle; 0 < e < 1 → ellipse; e = 1 → parabola; e > 1 → hyperbola. It is defined as e = c/a where c is the distance from centre to focus.
What is the latus rectum?: The latus rectum is the chord of a conic section that passes through the focus and is perpendicular to the major axis. For parabola y² = 4ax, length = 4a. For ellipse, length = 2b²/a.
How do you find the centre and radius from a general circle equation?: From x² + y² + 2gx + 2fy + c = 0, complete the square: centre = (−g, −f) and radius = √(g² + f² − c). The circle exists only when g² + f² − c > 0.

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