Use implicit differentiation to find an equation of the tangent line to the curve x^2+2xy-y^2+5x=3 at the poi

Question

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Use implicit differentiation to find an equation of the tangent line to the curve x^2+2xy-y^2+5x=3 at the point (1,3)

Give your answer in the form y=mx + b

Answer 1

x^2 + 2xy - y^2 + 5x = 3
Differentiate w.r.t. x:
2x + 2y + 2x dy/dx - 2y dy/dx + 5 = 0
=> dy/dx (2x - 2y) = -2x - 2y - 5
At (1, 3), we get
dy/dx (2-6) = -2 - 6 - 5
=> dy/dx = 13/4.
So the line is y = 13/4 (x-1) + 3
<=> y = 13/4 x - 1/4.