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

parabola

#1

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
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The slope of tangent line is the first derivative, that is
image
Because the tangent line is passed the point (2,-3), so we substitute x=2 and y=-3 into the above equation and get
image

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