Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0,0.5)

Question

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

Y=

Answer 1

2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)
at the point (0, 0.5)
0+y'=2*2*0.25*(4*0.5*y'-1)
y'=2y'-1
y'=1
Y=0.5+1*(X-0)
Y=X+0.5