### Home > CALC > Chapter 7 > Lesson 7.1.4 > Problem 7-44

7-44.

*y* = *x*^{2} + 2*x* + 4 has infinitely many tangent lines; two of them go through the origin.

Let the point of tangency be (*a*, *y*(*a*)) or (*a*, (*a*^{2} +2*a* + 4)).

Therefore, the slope of the tangent lines must be *y*'(*a*) = 2*a* + 2.

Of course, we do not know the value of '*a*' yet.

Write the equation of the tangent line(s) using Point-Slope form. Then solve for *y*. We will solve for '*a*' next.

Since we know that the lines pass through the origin, evaluate (*x*, *y*) for (0,0). This will give you the values of '*a*'.

Use the eTool below to explore the problem.

Click the link at right for the full version of the eTool: Calc 7-44 HW eTool