Answer:
a = 1, b = - 2
Explanation:
The points that lie on the curve and straight line satisfy the corresponding equations.
Substitute the points into their corresponding equations, that is
(1, - 1 ) → - a = 1² + b = 1 + b ( multiply both sides by - 1 )
a = - 1 - b → (1)
(3, 3 ) →
=
( cross- multiply )
- 3ab = 6 ( divide both sides by - 3 )
ab = - 2 → (2)
Substitute a = - 1 - b into (2)
(- 1 - b)b = - 2 , distribute left side
- b - b² = - 2 ( multiply through by - 1 )
b² + b = 2 ( subtract 2 from both sides )
b² + b - 2 = 0 ← in standard form
(b + 2)(b - 1) = 0 ← in factored form
Equate each factor to zero and solve for b
b + 2 = 0 ⇒ b = - 2
b - 1 = 0 ⇒ b = 1
Substitute these values into (1) for corresponding values of a
b = - 2 : a = - 1 - (- 2) = - 1 + 2 = 1
b = 1 : a = - 1 - 1 = - 2
Thus a = - 2, b = 1 or a = 1, b = - 2
Given that a > b then a = 1, b = - 2