我们知道,反比例函数y=k/x(k≠0)的图象是双曲线,由它的两条渐近线x轴、y轴互相垂直可知.方程xy=k(k≠0)表示的曲线是等轴双曲线.可以证明,将等轴双曲线C:x2-y2=a2(a0)绕坐标原点O按逆时针方向旋转45°,所得等轴双曲线C′的方程为xy=a22.事实上,设等轴双曲线C′的方程为xy=k(k We know that the image of the inverse proportional function y=k/x(k≠0) is a hyperbola, and its two asymptote lines, the x-axis and y-axis, are perpendicular to each other. The equation xy=k(k≠0) denotes The curve is an isometric hyperbola. It can be proved that the equiaxed hyperbola C:x2-y2=a2(a0) is rotated 45° counterclockwise around the origin O of the coordinate, and the resulting equation of the isometric hyperbola C′ is xy=a22. In fact, the equation for an isometric hyperbola C′ is xy=k(k