圆锥曲线

The conic family

Reflective and orbital properties

The polar conic equation

Graphing and standard forms

The eccentricity e discriminates the conic families. Which value gives a parabola?

For the ellipse x^2/a^2 + y^2/b^2 = 1 with a greater than b, the foci satisfy which relation?

A parabolic reflector works by which geometric property?

The polar equation r = ed/(1 + e cos theta) with e = 1/2 describes which conic?

Kepler's first law states that planets move in which conic with the sun at a focus?

For the ellipse r = ed/(1 + e cos theta), the perihelion occurs at theta = pi. As an expression, what is r there? Answer like ed/(1 + e).

For e greater than 1 the denominator 1 + e cos theta vanishes at cos theta = -1/e, giving the hyperbola's what? Answer with one word.

The general quadratic's discriminant B^2 - 4AC classifies conics. For the ellipse it is which sign? Answer with one word.

The conic discriminant B^2 - 4AC is zero for the parabola, positive for the hyperbola, and which sign for the ellipse? Answer with one word.

In the polar conic r = ed/(1 + e cos theta), the directrix sits at x equals which value? Answer with a single letter.