2 weird problems involving implicit differentiation

The first problem:

(x^2+y^2+5x)^2 = 25/2 (x^2+y^2) , find the equation of the tangent line to P(5,5)

1. y+ 1/3 x = 20/3

2. y = 1/3 x + 5/3

3. y+ 3x + 20/3 = 0

4. y + 1/3 x =5/3

5. y = 3x + 20/3

I always derive the eqn and plug in (5,5) but i always get a slope of -13/15 or something like that, and theres too much work to list out here, so i just really dont know

Problem 2:

A company manufacturing lawn mowers find that its weekly cost and demand equations are

C(x) = 40 + 24x, p(x) = 40 − x/4

when it sells x lawn-mowers per week. If the company can sell all the lawn-mowers it manufactures, determine the maximum profit from the sale of these lawn-mowers.

1. maximum profit = $211

2. maximum profit = $221

3. maximum profit = $201

4. maximum profit = $216

5. maximum profit = $206

I honestly have no idea where to start on this one

Thanks for anyone who helps!

Anthony