拋物線與雙曲線
開普勒把行星的軌道描述為橢圓，牛頓後來修改了這些橢圓，因為他指出這些軌道是特殊的圓錐截面，如拋物線和雙曲線。拋物線和雙曲線有許多相似之處，但也有區別，因為有不同的方程來解決涉及這些圓錐截面的幾何問題。為了更好地理解拋物線和雙曲線之間的區別，我們需要了解這些圓錐曲線。
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A section is a surface or the outline of that surface formed by cutting a solid figure with a plane. If the solid figure happens to be a cone, the resulting curve is called a conic section. The kind and shape of the conic section is determined by the angle of intersection of the plane and the axis of the cone. When the cone is cut at right angles to the axis, we get a circular shape. When cut at less than a right angle but more than the angle made by the side of the cone results in an ellipse. When cut parallel to the side of the cone, the curve obtained is a parabola and when cut nearly parallel to the axis that to the side, we get a curve known as hyperbola. As you can see from the figures, circles and ellipses are closed curves whereas parabolas and hyperbolas are open curves. In the case of a parabola, the two arms eventually become parallel to each other whereas in the case of a hyperbola it is not so.
因為圓和拋物線是通過在特定角度切割圓錐而形成的，所以所有的圓在形狀上是相同的，所有拋物線的形狀都是相同的。在雙曲線和橢圓的情況下，平面和軸之間的角度範圍很廣，這就是為什麼它們的形狀會有很大的變化。四種圓錐曲線的方程如下。
圓-x2+y2=1
橢圓-x2/a2+y2/b2=1
拋物線-y2=4ax
