Question 770902
(1) Try implicit differentiation of the ellipse equation and form from this the derivative for dy/dx for the ellipse.
(2) Find or read the slope of the line which is parallel to the tangents you want.
(3) Make an equation to equate the derivative with the needed slope value, and solve for x, likely for two values for x.  



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I did not actually solve the problem.  Only gave a description of process to solve.