Let a, b, c are such that the curve y = ax2 + bx + c is tangent to y = 3x – 3 at (1, 0) and is also tangent to y = x + 1 at (3, 4). Then

Engineering

Mathematics

Tangent and Normal

Question

Let a, b, c are such that the curve y = ax² + bx + c is tangent to y = 3x – 3 at (1, 0) and is also tangent to y = x + 1 at (3, 4). Then

2a – b – 4c = 9

ab = 2

2a + b = 3

a + c = – 4

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${\frac{dy}{dx}]}_{x = 1}$ = 2ax + b = 2a + b = 3 ….…(1)
and ${\frac{dy}{dx}]}_{x = 3}$ = 6a + b = 1 ….…(2)
(1) & (2)
⇒ a = $\frac{- 1}{2}$ ; b = 4 and c = $\frac{- 7}{2}$ .