### Home > CALC > Chapter 7 > Lesson 7.2.1 > Problem 7-62

7-62.

Find *a* so that the parabola *y* = *ax*^{2} + 3 is tangent to the line *y* = 5 − *x*. Also, state the point of tangency. Homework Help ✎

At the point of tangency *ax*^{2} + 3 = 5 − *x*

Since the tangent line is *y* = 5 − *x*, then the slope of the tangent is −1 at the point of tangency.

Therefore 2*ax* = −1.

Solve a system of equations.