Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
2x2 + xy + 2y2 = 5, (1, 1)
(ellipse)

The equation of the tangent line to the curve at the given point is

y = -x = 2

The formula for calculating the equation of a line in point-slope form is expressed as:

where:

m is the slope of the line

(x0, y0) is the point on the line

Given the equation

Differentiate the given equation implicitly to get the slope

Substitute m = -1 and the point (1, 1) into the equation of a line expressed as:

Hence the equation of the tangent line to the curve at the given point is

y = -x = 2

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step-by-step explanation:

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