Question -
Answer -
The given line is x – y + 5 = 0
y = x + 5 is the form of equation of a straight line y = mx + c,where m is the Slope of the line.
So the slope of the line is y = 1 × x + 5
So the Slope is 1. … (2)
Also the point (1, – 6) lie on the tangent, so
x = 1 & y = – 6 satisfies the equation, y = x3 +ax + b
– 6 = 13 + a × 1 + b
⇒ –6 = 1 + a + b
⇒ a+ b = – 7 … (3)
Since, the tangent is parallel to the line, from (1) & (2)
Hence, 3 + a = 1
⇒ a= – 2
From (3)
a + b = – 7
⇒ –2 + b = – 7
⇒ b= – 5
So the value is a = – 2 & b = – 5