Given:
The Slope of the tangent to the curve xy + ax + by = 2 at (1,1) is 2
First, we will find The Slope of tangent
we use product rule here,
since, The Slope of the tangent to the curve xy + ax + by = 2 at (1,1) is 2
⇒ – a – 1 = 2(1 + b)
⇒ – a – 1 = 2 + 2b
⇒ a + 2b = – 3 ...(1)
Also, the point (1,1) lies on the curve xy + ax + by = 2,we have
1 x1 + a x1 + b x1 = 2
⇒ 1 + a + b = 2
⇒ a + b = 1 ...(2)
from (1) & (2),we get
substitute b = – 4 in a + b = 1
a – 4 = 1
⇒ a = 5
So the value of a = 5 & b = – 4
