Question

求过已知切点的切线方程：已知函数y=x^2-x,求过(-2,0)的切线方程

Answer 1

切线方程

y= m(x+2) (1)

y= x^2-x (2)

sub (1) into (2)

m(x+2) = x^2-x

x^2-(1+m)x -2m =0

△=0

(1+m)^2 +8m=0

m^2+10m+1 =0

m = -5+2√6 or -5-2√6

切线方程

y= m(x+2)

where m= -5+2√6 or -5-2√6