Given that P is a point on the image of function y = 2 / x, and the distance from P to the origin is 2, how many points P are qualified?

Given that P is a point on the image of function y = 2 / x, and the distance from P to the origin is 2, how many points P are qualified?


The distance from P to the origin is 2
2^2=4=x^2+y^2=x^2+(2/x)^2
4x^2=x^4+4
(x^2-2)^2=0
x^2=2
x=±√2
There are two points of P: (√ 2, √ 2) and: (- √ 2, √ 2)



After the point P (M + 2,2m + 4) is shifted to the right several unit lengths, the point P '(4,6) is obtained, then the value of M is


2M+4=6
M=1



If P (M + 2,2m + 4) is shifted to the right by one unit length, the point P '(4,6) is obtained, then the value of M is equal to——


1



If the point P (M + 2,2m + 4) is shifted one unit to the right and P 'is on the y-axis, then the p' coordinate is_____ .


(0,-2)