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极坐标系和直角坐标系是两种不同的坐标系,两者既有区别,也有联系。有的数学题用直角坐标系解答显得方便;有的题用极坐标系解答显得方便;有的题,若综合利用两种坐标系来解答,则能起到互弥不足,相辅促成的作用。1991年高考数学(理)第26题,参考答案已给出利用直角坐标系求解的两种解法,笔者再利用极坐标系来求解,以供参考。题:双曲线的中心在坐标原点○,焦点在x轴上,过双曲线右焦点且斜率为(3/5)(1/2)的直线交双曲线于P、Q两点,若OP⊥OQ,
Polar coordinate systems and Cartesian coordinate systems are two different coordinate systems, and they are both distinct and related. Some mathematics questions are conveniently solved with rectangular coordinate systems; some are easily solved with polar coordinates; some questions, if used in combination with two coordinate systems, can play a role in mutual deficiency and complement each other. . In the 26th problem of mathematics (rational) in the college entrance examination in 1991, the reference solution has been given two solutions to solve using the rectangular coordinate system. The author then uses the polar coordinate system to solve for reference. Problem: The center of the hyperbola is at the origin of the coordinates ○, the focal point is on the x-axis, the right hyperfocus and the slope is (3/5) (1/2) of the straight line hyperbola at points P and Q. OQ,