SOLUTION: Find an equation of the tangent line to the graph at the given point. 7x^2-6(sq3)xy+13y^2-16=0. (sq3,1)

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7x^2-6(sq3)xy+13y^2-16 = 0


dy/dx = -(14x - 6sqrt(3)y)/(26y - 6sqrt(3)x)
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f'(sqrt(3),1) = -(14sqrt(3) - 6sqrt(3))/(26 - 18)
= - sqrt(3) slope of tangent line
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y = mx + b
1 = -3 + b
b = 4
--> y = -sqrt(3)*x + 4
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You can put this solution on YOUR website!


Differentiate the equation implicitly:





Use the Chain Rule and the Product Rule:





Now take out a common factor of 2 and then solve for



Do not succumb to the temptation to rationalize your denominator at this point. We have an expression for the tangent to your ellipse at any point, all that is needed now is to evaluate this expression at the given point. Substitute the coordinates of the given point for and in the expression for and do the arithmetic.

John

My calculator said it, I believe it, that settles it