Question

An equation of a tangent drawn to the curve $y=x^2-3x+2$ from the point $(1,-1)$ is

• A. $x+y=2$
• B. $3x+y=2$
• C. $y+x=0$
• D. $2y+x=-1$

Answer 1

The correct option is B $3x+y=2$

$(1,-1)$ does not lie on the parabola $y=x^2-3x+2$.
Let the slope of the tangent be $m$.
Then, equation of tangent is
$y-(-1)=m(x-1)$
or $y=mx-m-1$
Since, $y=mx-m-1$ is a tangent to the parabola $y=x^2-3x+2,$
$x^2-3x+2=mx-m-1$ should have equal roots.
$x^2-(m+3)x+(m+3)=0$
$D=0\Rightarrow (m+3{)}^2-4(m+3)=0$
$\Rightarrow m=-3,1$
Hence, equation of tangents are $y=-3x+2$ and $y=x-2$