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Angle between Two Lines

lf the curve ...

Question

lf the curve $y = p x^{2} + q x + r$ passes through the point (1, 2) and the line $y = x$ touches it at the origin, then the values of $p, q$ and $r$ are

p = 1, q = - 1, r = 0

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p = 1, q = 1, r = 0

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p = - 1, q = 1, r = 0

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p = 1, q = 2, r = 3

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Solution

The correct option is D $p = 1, q = 1, r = 0$
$2 = p + q + r$
$r = 0$
$\frac{d x}{d y} |_{x = 0} = 1$
$\frac{d y}{d x} = 2 p x + q$
$q = 1$
$2 = p + 1 + 0$
$p = 1$

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