We have to find the equations of both lines through the point (2,-3) that are tangent to the parabola `y=x^2+x`

i.e. `m=y'=2x+1`

Now we find two points on the two tangent lines to y using: `(x,x^2+x)` and (2,-3). This is to show that (x,f(x)) is a point on the original equation f(x).

Now we have to find the slope of these two points and equate it to the derivative or slope of the original equation.

i.e. `2x+1=\frac{x^2+x+3}{x-2}`

i.e. `\mathbf{y=-x-1}`

So the equation of the two tangent lines to the parabola `y=x^2+x` passing through the point (2,-3) are:

The slope of the line tangent...

(The entire section contains 3 answers and 572 words.)

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