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### Assignment 8

The line:

intersects the parabola:

in two points en .

The tangent lines at these points intersect in a point .

Calculate the coordinates of .

### Solution

First we calculate the intersection points, thus we have to solve the following equation:

We rewrite this:

and we can solve this equation by factorizing:

and thus:

or

The corresponding intersection points are:

and

In order to determine the slopes of the tangent line(s) at these points we have to differentiate the function of the parabola:

For the slope of the tangent line at we find and for the one at we find . The equation of one tangent line is:

or:

The equation of the other tangent line is:

or:

We find the intersection point of these tangent lines by solving the equation:

The solution of the equation is and the corresponding -value is . The point has the coordinates .

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