Conic curve formula: ellipse

1, elliptic standard equation with the center at the origin and the focus at the X axis: where x? /a？ +y？ /b？ = 1, where a >；; b & gt0，c？ =a？ -B?

2. Elliptic standard equation with the center at the origin and the focus at the Y axis: Y? /a？ +x？ /b？ = 1, where a >；; b & gt0，c？ =a？ -B?

Parametric equation: x=acos? ; y=bsin？ (? Is the parameter 0? 2? )

Conic curve formula: hyperbola

1, hyperbolic standard equation with center at origin and focus on X axis: X? /a-y？ /b？ = 1, where a >；; 0，b & gt0，c？ =a？ +b？ .

2. Hyperbolic standard equation with the center at the origin and the focus on the Y axis: Y? /a？ -x？ /b？ = 1, where a >；; 0，b & gt0，c？ =a？ +b？ .

Parametric equation: x=asec? ; y=btan？ (? As a parameter)

Conic curve formula: parabola

Parametric equation: x=2pt? ; Y=2pt(t is the parameter) t= 1/tan? (Tan? Determine that slope of the straight line for the point on the curve and the coordinate origin) in particular, t can be equal to 0.

Cartesian coordinates: y=ax? +bx+c (opening direction is y axis, a? 0)x=ay？ +by+c (opening direction is x axis, a? 0)

weird

Ellipse, hyperbola and parabola all have a unified definition: on the plane, the locus of a point whose distance to a fixed point is constant compared with the distance to a fixed line e is called a conic curve. While 0 1 is a hyperbola.

Summary of knowledge points of cone formula

Conic curve ellipse hyperbola parabola

Standard equation x? /a？ +y？ /b？ = 1(a >b & gt0) x？ /a？ -Really? /b？ = 1(a >0，b & gt0) y？ = 2px(p & gt； 0)

Range x? [-a，a] x？ (-? ，-a]？ 【a，+？ )x？ [0,+? )

y？ [-b，b] y？ R y？ rare

About x axis, y axis symmetry, origin axis symmetry about x axis, y axis symmetry about x axis.

Vertex (a, 0), (a, 0), (0, b), (0, -b) (a, 0), (-a, 0) (0, 0)

Focus (c, 0), (-c, 0) (c, 0), (-c, 0) (p/2, 0)

Where is c? =a？ -B? Where is c? =a？ +b？

Directline x= a? /c x=？ Answer? /c x=-p/2

Asymptote y=? (b/a)x？

Eccentricity e=c/a, e? (0， 1) e=c/a，e？ ( 1,+? )e= 1

∣ The focal radius of PF? ∣=a+ex ∣PF？ ∣=∣ex+a∣ ∣PF∣=x+p/2

∣PF？ ∣=a-ex ∣PF？ ∣=∣ex-a∣

Focal length p=b? /c p=b？ /c p

Diameter 2b? /a 2b？ /a 2p

Parameter equation x=a? Because? x=a？ sec？ x=2pt？

y=b？ Sin? ,? Is the parameter y=b? Tan? ,? Is the parameter y = 2pt, and t is the parameter.

What is the point x0 on the conic section? x/a？ +y0？ y/b？ = 1 x0x/a？ -What about you? y/b？ = 1 y0？ y=p(x+x0)

The tangent equation of (x0, y0)

The tangent equation with slope k y=kx(ak? +b？ )y=kx(ak？ -B? )y=kx+p/2k