Y=4/x的图象绕点0旋转45度以后的图像方程?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 05:54:53
![Y=4/x的图象绕点0旋转45度以后的图像方程?](/uploads/image/z/14570681-41-1.jpg?t=Y%3D4%2Fx%E7%9A%84%E5%9B%BE%E8%B1%A1%E7%BB%95%E7%82%B90%E6%97%8B%E8%BD%AC45%E5%BA%A6%E4%BB%A5%E5%90%8E%E7%9A%84%E5%9B%BE%E5%83%8F%E6%96%B9%E7%A8%8B%3F)
Y=4/x的图象绕点0旋转45度以后的图像方程?
Y=4/x的图象绕点0旋转45度以后的图像方程?
Y=4/x的图象绕点0旋转45度以后的图像方程?
设y=4/x 上的任意点(a,b), ab=4,它到原点距离为r, 与原点连线后, 连线与X轴形成的夹角为θ. 则
a = r cosθ
b = r sinθ
点(a,b) 旋转45度后 ,点的坐标为(x,y)
x = rcos(θ + π/4) = rcosθ cos(π/4) - rsinθsin(π/4)
= (√2 /2)(a - b)
√2x = a - b
y = r sin(θ+ π/4) = rsinθcos(π/4) + rcosθsin(π/4)
= (√2 /2) (a + b)
√2y = a + b
以上两式相加和相减:
√2y - √2x = 2 b
√2y +√2 x = 2 a
以上两式相乘:
( √2y - √2x )( √2y + √2x )=4ab=4 x 4 = 8
2y^2 - 2x^2 = 8
y^2 - x^2 = 4
是条标准的双曲线。分逆时针和顺时针旋转两种情况
逆时针 45°
y²-x² = 4
顺时针 45°
x²-y² = 4