Not necessarily a typo. The point (5, 25) is not on the parabola but there exist a line through (5, 25) that **is** tangent to the parabola at some other point. Any line through (5, 25) is of the form y= m(x- 5)+ 25 for some slope, m. That will be tangent to the parabola \(\displaystyle y= 2x^2\) where \(\displaystyle 4x= m\) and \(\displaystyle m(x- 5)+ 25= 2x^2\). So we have two equations to solve for m and x.

Since 4x= m, \(\displaystyle 4x(x- 5)+ 25= 4x^2- 20x+ 25= 4x^2\). That is, 20x= 25 so x= 5/4. Then m= 4x= 4(5/4)= 5. The line y= 4(x- 5)+ 25= 4x+ 5 passes through the point (5 25) and is tangent to the parabola \(\displaystyle y= 2x^2\) at \(\displaystyle \left(\frac{5}{4}, \frac{25}{8}\right)\).