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Question -

Find the values of a and b if the Slope of the tangent to the curve x y + a x + by = 2 at (1, 1) is 2.



Answer -


 –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 × 1 + a × 1 + b × 1 = 2

 1+ a + b = 2

 a+ b = 1 … (2)

From (1) & (2), we get b = -4

Substitute b = – 4 in a + b = 1

a – 4 = 1

 a= 5

So the value of a = 5 & b = – 4

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