In the $xy$-plane, a line with equation $y=3a$, for some constant $a$, intersects a parabola at exactly one point. If the parabola has equation$y=x^2-4x-5$, what is the value of $a$?
Answer:
-3
Explanation
The correct answer is $-3$.
Substitute $y$ from the first equation into the second equation and then find $a$ for which there is exactly one solution for the equation.
✨ Expert's Tip ✨
A quadratic equation has no real root if the discriminant, $D = b^2 - 4ac$, is less than zero.
