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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
.
Return to Assignments Tangent line to graph