Find the equation of the locus of the mid-point of the chord ofth_数学解答

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

人气：229 ℃　时间：2020-05-12 06:21:57

解答

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请问你的(4c/5, -c/5)是怎样算出来的？