(x 2/a 2)-(y 2/b 2) = 1 (focus x axis) (y 2/a 2)-(x 2/b 2) = 1 (focus y axis): hyperbola.
Y 2 = 2px (focus X positive) y 2 =-2px (focus X negative) x 2 = 2py (focus Y positive) x 2 =-2py (focus Y negative): parabola.
Directrix: ellipse and hyperbola: x = (a 2)/c
Parabola: x=p/2 (take y 2 = 2px as an example)
Focus radius:
Ellipse and hyperbola: a ex (e is eccentricity. X is the abscissa of this point, with a plus sign for less than 0 and a minus sign for more than 0).
Parabola: p/2+x (take y 2 = 2px as an example)
The ellipse and hyperbola above take the focus on the X axis as an example.
Chord length formula: let the slope of the straight line where the chord is located be k, then the chord length = root sign [(1+k2) * (x1-x2) 2] = root sign [(1+k2) * ((x1+x2)). We can know x 1+x2 and x 1*x2 by Vieta theorem, and then substitute them into the formula to get the chord length.
Parabolic path =2p
Parabolic focal chord length =x 1+x2+p By using focus chord's equation and quadratic equation, a quadratic equation about x is obtained by eliminating y, where x 1 and x2 are two equations.