The focus is on the x axis; B>a>0 focus on Y axis): ellipse

(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 is positive) y 2 =-2px (focus x is negative)

X 2 = 2py (focus y is positive)

X 2 =-2py (negative focus y): 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: an example

(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+k 2) * ((x 1+x2)).

Connect the equation of conic curve with the equation of straight line, eliminate y to get a quadratic equation about x, where x 1 and x2 are two equations, then 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 equation and conic equation, we can get a quadratic equation about x by eliminating y, where x 1 and x2 are two equations.