The equation of an ellipse is x^2+y^2/4=1. The equation of a line is y=3x+b. For what values of b is the line tangent to the ellipse?
Substitute \(y=3x+b\) into the first equation:
In order for the line to be tangent to the ellipse, the above quadratic in terms of x must have exactly one solution, meaning that the discriminant has to be zero. Therefore,