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Global Maxima

The line y=...

Question

The line $y = (2 x + a)$ will not intersect the parabola $y^{2} = 2 x$ if

a < \frac{1}{5}

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a > \frac{1}{4}

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a = \frac{1}{3}

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a = - 3

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Solution

The correct option is C $a > \frac{1}{4}$
$(2 x + a)^{2} = 2 x$
$4 x^{2} + 4 a x + a^{2} = 2 x$
$4 x^{2} + x (4 a - 2) + a^{2} = 0$
$D < 0$
$(4 a - 2)^{2} - 4 (4) (a^{2}) < 0$
$16 a^{2} + 4 - 16 a - 16 a^{2} < 0$
$a > \frac{1}{4}$

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a

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