Question

find the values of a and b if the slope of the tangent to the curve xy + ax + b y = 2 at 1, 1 is 2

Answer 1

x dy/dx + y + a + b dy/dx = 0
dy/dx = 2
2 * 1 +  1 + a + 2b = 0 3 + a + 2b = 0
a + 2b = -3 ------- (i)
Given (1,1) so
1 + a + b = 2
a + b = 1 ---- (ii)
On solving (i) and (ii) we have
a + 2b = -3 a + b = 1----------------  b = - 4
a - 8 = -3
a = 5