A-Maths problemA line segment PQ is 5 units long.The end point P moves along the x-axis while the end point Q moves along the y-axis.R is the point on PQ such that PR:RQ=2:3.Find the equation of the locus of R.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/20 01:08:22
A-MathsproblemAlinesegmentPQis5unitslong.TheendpointPmovesalongthex-axiswhiletheendpointQmovesalongt

A-Maths problemA line segment PQ is 5 units long.The end point P moves along the x-axis while the end point Q moves along the y-axis.R is the point on PQ such that PR:RQ=2:3.Find the equation of the locus of R.
A-Maths problem
A line segment PQ is 5 units long.The end point P moves along the x-axis while the end point Q moves along the y-axis.R is the point on PQ such that PR:RQ=2:3.Find the equation of the locus of R.

A-Maths problemA line segment PQ is 5 units long.The end point P moves along the x-axis while the end point Q moves along the y-axis.R is the point on PQ such that PR:RQ=2:3.Find the equation of the locus of R.
设R坐标为(x,y)
则由题意可知:
P(5x/3,0)
Q(0,5y/2)
而由|PQ|=5
可知(5x/3)^2+(5y/2)^2=25
这就是动点R的方程,为一个椭圆.