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# Solution for If the Line Y = X Touches the Curve Y = X2 + Bx + C at a Point (1, 1) Then (A) B = 1, C = 2 (B) B = −1, C = 1 (C) B = 2, C = 1 (D) B = −2, C = 1 - CBSE (Commerce) Class 12 - Mathematics

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#### Question

If the line y = x touches the curve y = x2 + bx + c at a point (1, 1) then
(a) b = 1, c = 2
(b) b = −1, c = 1
(c) b = 2, c = 1
(d) b = −2, c = 1

#### Solution

(b) b = −1, c= 1
We can find the slope of the line by differentiating w.r.t. x.
Slope of the given line = 1
Now,

$y = x^2 + bx + c . . . \left( 1 \right)$

$\Rightarrow \frac{dy}{dx} = 2x + b$

$\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 1, 1 \right) =2+b$

$\text { Given}:$

$\text { Slope of the tangent } = 1$

$\Rightarrow 2 + b = 1$

$\Rightarrow b = - 1$

$\text { On substituting b= - 1, x=1 and y=1 in (1), we get}$

$\Rightarrow 1 = 1 - 1 + c$

$\Rightarrow c = 1$

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Solution If the Line Y = X Touches the Curve Y = X2 + Bx + C at a Point (1, 1) Then (A) B = 1, C = 2 (B) B = −1, C = 1 (C) B = 2, C = 1 (D) B = −2, C = 1 Concept: Tangents and Normals.
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