论文部分内容阅读
在十年制统编教材高中第二册中,我们知道二次曲线统一的极坐标方程是:ρ=ep/(1-ecosθ)(1)其中p是焦点是准线的距离,即焦距。e是二次曲线的离心率,当e<1时,曲线为椭圆,当e>1时,曲线为双曲线;当e=1时,曲线为抛物线。把二次曲线的极坐标方程(1)化成标准直角坐标方的程一般方法是: 由(1)得:ρ-eρcosθ=ep,ρ=ex+ep ∴ρ~2=e~2x~2+2e~2px+e~2p~2, ∴x~2+y~2=e~2x~2+2e~2px+e~2p~2 ∴(1-e~2)x~2+y~2-2e~2px-e~2p~2=0 (2) (1)当e=1时,方程(2)变成;
In the second edition of the ten-year textbook, we know that the polar equation of the quadratic curve is: ρ=ep/(1-ecos θ) (1) where p is the distance from the focus to the quasi-line, that is, the focal length. e is the eccentricity of the quadratic curve. When e<1, the curve is an ellipse. When e>1, the curve is a hyperbola; when e=1, the curve is a parabola. The general method of converting the polar coordinate equation (1) of the quadratic curve to the standard rectangular coordinate is: From (1): ρ-eρcosθ=ep,ρ=ex+ep ∴ρ~2=e~2x~2+ 2e~2px+e~2p~2, ∴x~2+y~2=e~2x~2+2e~2px+e~2p~2 ∴(1-e~2)x~2+y~2- 2e~2px-e~2p~2=0 (2) (1) When e=1, equation (2) becomes;