Conic Sections

Board: GSEB Class: 11

Chapter Overview

Conic sections are defined geometrically and algebraically. A circle is all points equidistant from a center. A parabola is all points equidistant from a focus and directrix. An ellipse has constant sum of distances to two foci. A hyperbola has constant absolute difference of distances to two foci.

Standard equations, foci, directrices, eccentricity, and latus rectum are covered for each conic.

Topics Covered

Circle Equation
Parabola - Focus and Directrix
Ellipse - Foci and Vertices
Hyperbola - Foci and Asymptotes
Eccentricity
Latus Rectum

Key Formulas

Circle: (x-h)2 + (y-k)2 = r2

Parabola: y2 = 4ax

Ellipse: x2/a2 + y2/b2 = 1

Hyperbola: x2/a2 - y2/b2 = 1

e = √1 - b2/a2 for ellipse

e = √1 + b2/a2 for hyperbola

Real-World Applications

Applications: Satellite dishes, telescopes (parabolas), planetary orbits (ellipses), GPS navigation (hyperbolas).

Study Tips

Tip: Compare standard equations side by side

Tip: Understand how eccentricity distinguishes conics

Tip: Practice sketching each conic