Find the equation of the locus of the mid-point of the chord

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/12 01:10:30

Find the equation of the locus of the mid-point of the chord of
the curve x²+4y²=1 with gradient 1.

x^2+4y^2=1与x=y+c的交点为5y^2+2cy+c^2-1=0, 5x^2-8cx+4c^2-1=0.
所以中点为(4c/5, -c/5)
所以中点的曲线a(t)=(4t/5, -t/5),或x+4y=0
再问：请问你的(4c/5, -c/5)是怎样算出来的？

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