Question

If the line 2x – y + 7 = 0 touches the curve y = ax² + bx + 5 at (1, 9) then the values of ‘a’ and ‘b’ are ______.

Options

• 2, 6

• 2, –6

• –2, 6

• 3, 2

Answer 1

If the line 2x – y + 7 = 0 touches the curve y = ax² + bx + 5 at (1, 9) then the values of ‘a’ and ‘b’ are –2, 6.

Explanation:

y = ax² + bx + 5

∴ `dy/dx` = 2ax + b

∴ `(dy/dx)_((1"," 9))` = 2a + b

= Slope of tangent at (1, 9)

But 2x – y + 7 = 0 is the equation of tangent whose slope is 2

∴ 2a + b = 2   ...(1)

The point (1, 9) lies on y = ax² + bx + 5

∴ 9 = a + b + 5

∴ a + b = 4    ...(2)

Solving (1) and (2):

2a + b = 2
  a + b = 4
–   –      –   
  a       = –2

∴ b = 6