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Mentallic

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## Homework Statement

I am given the parabola [tex]y=\frac{x^2}{2}[/tex]

I need to find the equations of the 2 tangents to the parabola that pass through the point A(5,-2)

## Homework Equations

[tex]y-y_{1}=m(x-x_{1})[/tex]

[tex]a = \frac{1}{2}[/tex]

therefore: tangents pass through the points [tex]P(p,\frac{p^{2}}{2})[/tex] and [tex]Q(q,\frac{q^{2}}{2})[/tex]

[tex]\frac{dy}{dx}=x[/tex]

## The Attempt at a Solution

I began to check if the given point was outside the parabola

i.e. [tex]y_{1}<\frac{x^{2}_{1}}{2}[/tex]

[tex]-2<\frac{5}{2}[/tex] therefore, the point lies outside the parabola and there are 2 lines that will pass through the point, and are a tangent to the parabola.

[tex]y+2=m(x-5)[/tex] where there are 2 values of m, each intersecting the parabola only once. i.e. tangent to parabola.

From here I am totally stumped. I can't use the 1st derivative as I don't know the x value for which the gradient will pass through the point.

Any help would be much appreciated.

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