# Use implicit differentiation to find an equation of the tangent line to the cardioid

1. Feb 23, 2010

### winslow

1. The problem statement, all variables and given/known data
Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0, 0.5).

x2 + y2 = (2x2 + 2y2 - x)2

2. Relevant equations

Derivative rules
point slope formula

3. The attempt at a solution

I got

y' = [16x3-4x2+16xy2-4y2-4y2-8x2+2x] / [2y - 16x2y-16y3+8xy]

Now the equation of the tangent line should come out to y = x + (1/2)

Not sure exactly how it gets that I know you use point slope formula once you find the slope but I'm not sure how to simplify that down

2. Feb 24, 2010

### Staff: Mentor

Re: Use implicit differentiation to find an equation of the tangent line to the cardi

I'll take your word that the above is correct. Now evaluate the right side at (0, 1/2). That gives the slope of the tangent line to the cardioid at that point.

After you have this value, use the point-slope form of the equation of a line to get the equation of the tangent line.