Question

Find the equation of the tangent line to the curve $y=x^2-2x+7$ which is parallel to the line $2x-y+9=0$

Answer 1

Differentiating the equation of the curve with respect to $x$, we get
$\frac{dy}{dx}=2x-2$
Since the tangent line is parallel to $2x-y+9=0$,
$\frac{dy}{dx}=$slope of the straight line$=2$
$\Rightarrow 2x-2=2$
$\Rightarrow x=2$
Substituting $x=2$ in the equation of the curve, we get $y=7$
Hence, equation of tangent at $(2,7)$ with slope $2$ is
$y-7=2(x-2)$
$\Rightarrow 2x-y+3=0$