# Implicit Differentiation and Tangent Lines

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

$x^2 + y^2 = (2x^2 + 2y^2 - x)^2$

Point: $(0, 1/2)$

The graph is cardioid.

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Differentiate implicitly and get $2x+2y\frac{dy}{dx}=2(4x+4y\frac{dy}{dx}-1)(2x^2+2y^2-x)$.Now, find $\frac{dy}{dx}$ at the given point which is the gradient of the tangent line. Then use the equation of a straight line $y=mx+c$ to obtain the desired equation of the tangent.