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Slope Form a Line

If the line x...

Question

If the line $x + y - 1 = 0$ touches the parabola $y^{2} = k x,$ then the value of $| k |$ is

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Solution

If $y = - x + 1$ is tangent to $y^{2} = k x$ then
using $c = \frac{a}{m}$
$1 = \frac{k / 4}{- 1}$
$\Rightarrow k = - 4 ∴ | k | = 4$

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