Question

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

Answer 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