When the straight line L intersects the X-axis, we take the X-axis as the reference. The angle a formed between the positive direction of the X-axis and the upward direction of the straight line L is called the inclination angle of the straight line L.

When the straight line L is parallel to or coincident with the X-axis, its inclination angle is 0°.

The value range of the inclination angle a of a straight line is [0, 180°)

The tangent of the inclination angle a ( ) of a straight line L is called the slope of the straight line. The slope is usually represented by the lowercase letter K, that is, K=tana.

The slope formula of the straight line passing through two points P1(x1, y1), P2(x1, y1).x1≠x2 is K=

①Geometric method: d>r

②Algebraic method: △<0

①Geometric method: d=r

②Algebraic method: △=0

①Geometric method: d＜r

②Algebraic method: △＞0

①Geometric method: d>R+r

②Algebraic method: no real number solution

③Number of common tangent lines: 4

①Geometric method: d＝R＋r

②Algebraic method: a set of real solutions

③Number of common tangent lines: 3

①Geometric method: R－r＜d＜R+r

②Algebraic method: two sets of real number solutions

③Number of common tangent lines: 2

①Geometric method: d=R-r

②Algebraic method: a set of real solutions

③Number of common tangent lines: 1

①Geometric method: d=R-r

②Algebraic method: no real number solution

③Number of common tangent lines: 0

(2) Circle system equation

The locus of a point in the plane where the sum of the distances from two fixed points F1 and F2 is equal to a constant (greater than |F1 F2|

Two fixed points F1, F2

The distance between the two focal points |F1 F2|

half the focal length

The locus of a point in the plane where the absolute value of the difference in distance from two fixed points F1 and F2 is equal to a non-zero constant (less than |F1 F2|)

| |MF1|－|MF2| |=2a (constant) (0＜2a＜|F1 F2|)

Two fixed points F1, F2

The distance between two foci, expressed as |F1 F2|

The locus of a point in the plane at a distance from a fixed point F and a straight line l (l does not pass through point F)

Point F is called the focus of the parabola

The straight line l is called the directrix of the parabola