Find the equation of tangents drawn to the parabola `y=x^2-3x+2` from the point `(1,-1)dot`

Explanation

Tangents are drawn to the parabola from the point (1,-1). Now, the equation of line from (1,-1) having sllope m is `y-(-1)=m(x-1)`
`ory=mx-m-1`
Since this touches the parabola, when we slove line and parabola, the resulting quadratic will have equal roots.
Sloving, we have
`mx-m-1=x^(2)-3x+2`
`orx^(2)-(3+m)x+3+m=0`
This equation has equal root, i.e.,
`(m+3)^(2)-4(m+3)=0`
`i.e.," "m=-3orm=1`
`y+1=-3(x-1)andy+1=x-1`
`or 3x+y-2=0andx-y-2=0`