Conic curve has always been a difficult point in college entrance examination. It is suggested to memorize the equations of ellipse, parabola and hyperbola, do more corresponding exercises and carefully check the problem-solving steps of research standards. Even if you can't, you should have a general idea of what to write at each step. Don't leave a topic, at least write out the formula first.
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More than 2000 years ago, ancient Greek mathematicians first began to study conic curves, and achieved a lot of results. Apollonius, an ancient Greek mathematician, studied these curves with the method of plane truncated cone.
Cut the cone with a plane perpendicular to the axis of the cone and you get a circle; Tilt the plane gradually to get an ellipse; When the plane is inclined to "and only parallel to a generatrix of the cone", a parabola is obtained; A branch of a hyperbola can be cut with a plane parallel to the axis of a cone.
Linear parametric equation: x=x+tcosθ y=y+tsinθ (t is the parameter).
Cyclic parameter equation: x=X+rcosθ y=Y+rsinθ (θ is the parameter).
Elliptic parameter equation: x=X+acosθ y=Y+bsinθ (θ is the parameter).
Hyperbolic parametric equation: x=X+asecθ y=Y+btanθ (θ is the parameter).
Parabolic parameter equation: x = x = x=2pt^2 y=2pt (t t t is the parameter).
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