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Write the equation of the line(s) tangent to that pass through the origin. .

has infinitely many tangent lines; two of them go through the origin.

Let the point of tangency be or .

Therefore, the slope of the tangent lines must be .
Of course, we do not know the value of '' yet.

Write the equation of the tangent line(s) using Point-Slope form. Then solve for . We will solve for '' next.

Since we know that the lines pass through the origin, evaluate for . This will give you the values of ''.

Use the eTool below to explore the problem.
Click the link at right for the full version of the eTool: Calc 7-41 HW eTool