📐

Conic Sections

★★★☆☆High School

📖Definition

Curves formed by intersecting a cone with a plane: circle, ellipse, parabola, and hyperbola.

x² + y² = r²

Circle (centered at origin)

(x²)/(a²) + (y²)/(b²) = 1

Ellipse (centered at origin)

y = ax² + bx + c or x² = 4py

Parabola

(x²)/(a²) - (y²)/(b²) = 1

Hyperbola (centered at origin)

예제 1★★☆☆☆

Find the major and minor axis lengths of ellipse x²/9 + y²/4 = 1.

예제 2★★★☆☆

Find the focus of parabola y = x².

Discovered by: Apollonius of Perga (c. 200 BCE)

Apollonius systematically studied conic sections.

Planetary orbits

Satellite dishes, reflectors

#geometry#conic#analytic#advanced