find the values of p and q if slope of the tangent to the curve xy + pq + qy = 2(1, 1) is 2

Answer 1

xy' + y + qy' = 0
y' = -y/(x+q)
at (1,1) y' = -1/(1+q) = 2
so, q = -3/2

so, at (1,1)
1 - 3/2 p - 3/2 = 2
p = -5/3

xy + 5/2 - 3y/2 = 2
and the tangent line is
y-1 = 2(x-1)

visit wolframalpha.com and enter

plot xy + 5/2 - 3y/2 = 2, y-1 = 2(x-1), x=0..2

Answer 2

Good answer.