If at x = 1, y = 2x is tangent to the parabola $y = a x^{2} + b x + c$ , then respective values of a, b, c are

\frac{1}{2}, 1, \frac{1}{2}

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1, \frac{1}{2}, \frac{1}{2}

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\frac{1}{2}, \frac{1}{2}, 1

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1, 1, \frac{1}{2}

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Solution

The correct option is A $\frac{1}{2}, 1, \frac{1}{2}$
$F o r x = 1, y = a + b + c$
Tangent at $(1, a + b + c) i s \frac{1}{2} (y + a + b + c) = a x + \frac{b}{2} (x + 1) + c$
Comparing with $y = 2 x, c = a, b = 2 (1 - a)$

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