How do you find the coordinates of the points on the curve x2−xy+y2=9 where the tangent line is vertical?

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Balraj Conrad · Accepted Answer

Explanation:  Find dydx using implicit differentiation.  dydx=−y−2xx−2y  The tangent will be vertical when dydx approaches ∞ , which happens at y=12x  Now substitute 12x for y in the original equation and solve to get x=±23.  Finish by using y=12x to get the y coordinates.  So the points are (23,3)and(−23,−3)

Asa Buck · Accepted Answer

x2+y2−xy−9=0. represents an ellipse.In the standard form, this is(x+y)236+(x−y)212=1Let us find x′=dxdy.2xx&#039;+2y-x&#039;y-x=0, giving for the vertical direction2y=x, when x′=1y′=1∞=0.Substituting in the equation,x2+x24−x22=9, giving x=±3.The points of contact fo the tangents are ±3(1,2).So, the vertical tangents are x=±23.

How do you find the coordinates of the points on

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