Question

把曲线x^2-y^2+2x=0变成曲线x^2-16y^2+4x=0的伸缩变换是

Answer 1

化简下就知道了

x^2-y^2+2x=0->(x+1)^2-y^2=1

x^2-16y^2+4x=0->(x+2)^2-(4y)^2=4

所以(x+2)^2-(4y)^2=4->(x/2+1)^2-(2y)^2=1

所以x轴收缩为原1/2 y轴放大为原来2倍