①

When the straight line AB is out of focus, x 1x2 =

p？ /4

y 1y2 =

-p？ ;

(when a and b are on parabola x? =2py, with x 1x2 =

-p？

y 1y2 =

p？ /4

Only when a straight line passes through the focus can it be established)

②

Chord length of focal length: |AB|

=

x 1+x2+P

=

2P/[(sinθ)2]=(x 1+x2)/2+P；

③

( 1/|FA|)+( 1/|FB|)=

2/P； (The long one is P/( 1-cosθ), and the short one is P/( 1+cosθ))

④ If OA is perpendicular to OB, AB crosses the fixed point M(2P, 0);

⑤ Focus radius: |FP|=x+p/2

(The distance from the point P on the parabola to the focus F is equal to the distance from the point P to the directrix L);

⑥ chord length formula: ab = √ (1+k2) * │ x1-x2 │;

⑦△= B2-4ac；

⑴△= B2-4ac & gt； 0 has two real roots;

(2) = B2-4ac = 0 has two identical real roots;

⑶△= B2-4ac & lt； 0 has no real root.

⑧ The distance from the focus of a parabola to its tangent perpendicular is the median term of the ratio of the focus to the tangent point and vertex;

(9) The tangent of the standard parabola at (x0, y0) is yy0=p(x+x0).

(Note: X in the tangent equation of conic curve? =x*x0

，y？ =y*y0，x=(x+x0)/2

y=(y+y0)/2

)

Extended data:

(1) Know that the parabola passes through three points (x 1, y 1)(x2, y2)(x3, y3) Let the parabola equation be y=ax? +bx+c, substitute the coordinates of each point to get the ternary linear equations, and get the values of a, b and c to get the analytical formula.

(2) Know the two intersections (x 1, 0) and (x2, 0) of the parabola and the X axis, and know that the parabola passes through a certain point (m, n). Let the equation of parabola be y=a(x-x 1)(x-x2), and then put the point (m, n).

(3) Given the symmetry axis x=k, let the parabolic equation be y=a(x-k)? +b, and then determine the values of a and c by combining other conditions.

(4) Given that the maximum value of quadratic function is p, let the parabolic equation be y=a(x-k)? +p, a, k should be determined according to other conditions.

References:

Sogou encyclopedia-parabola