Question

数学题“椭圆ax平方+by平方=1,与直x+y-1=0交于A.B两点,C是AB的中点,|AB|=2根号2,kOC=2分之

Answer 1

设A(x1,y1),B(x2,y2),a（x1-x2）（x1+x2）+b（y1-y2）（y1+y2）=0,（y1-y2）/（x1-x2）=-1,kOC=a/b=√2/2,（√2）a=b,ax^2+（√2）ay^2=1,x+y-1=0联立,由/AB/=√2,解得a=1/3,所以椭圆为x^2/3+√2y^2/3=1