A3. Which tangent to the parabola with the equation $y=x^{2}+x+9$ is parallel to the line with the equation $-4 x+2 y-5=0$ ?
(A) $4 x-8 y+37=0$
(B) $4 x-8 y-37=0$
(C) $8 x-4 y-35=0$
(D) $-4 x-8 y+37=0$
(E) $8 x-4 y+35=0$
A3. We write the equation $x^{2}+x+9=2 x+n$ and transform it into the form $x^{2}-x+9-n=0$. Then we consider the condition that the quadratic equation has one double real solution if the value of the discriminant of the quadratic equation is equal to $0$. We apply this condition by substituting the values of the parameters and get the equation $1-4(9-n)=0$. The solution to this equation is $n=\frac{35}{4}$, and thus the equation of the tangent is $8 x-4 y+35=0$. The correct answer is $E$.