The graph of the equation 2x2 + xy + y2 = 4 is the tilted ellipse pictured below

Question

The graph of the equation 2x2 + xy + y2 = 4 is the tilted ellipse pictured below; i.e. the points (x,y) in the plane that satisfy the equation yield the pictured point P=(1,-2) is on the ellipse and the tangent through P is also pictured. If m is the slope of the tangent line, then using the slope/point formula, the equation of the tangent line will be: Simultaneously solve the equation of the tangent line and ellipse to arrive at this quadratic in x: Use the reasoning in class and the quadratic formula to determine that m =

Explanation / Answer

answer is 2/3. i used calculus.

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