**Find equations of both lines through the point (2,-3) that are tangent to the parabola y = x2 + x.**

**y = …(smaller slope)**

**y = …(larger slope)**

**Answer:**

First, we let the coordinates of the point on the parabola is (m,n)

Then we will have the equation

The slope of tangent line is the first derivative, that is

Because the tangent line is passed the point (2,-3), so we substitute x=2 and y=-3 into the above equation and get

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