Question:
<p>The set of points (x, y) whose distance from the line y = 2x + 2 is the same as the distance from (2, 0) is a parabola. This parabola is congruent to the parabola in standard form y = Kx<sup>2</sup> for some K which is equal to :</p>
<p style="display:inline"><span class="math-tex">\(\frac{4}{\sqrt{5}}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{12}{\sqrt{5}}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{\sqrt{5}}{4}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{\sqrt{5}}{12}\)</span></p>
Step-by-Step Solution
Key Concept: The congruence of any parabola is determined by its focal length, where the perpendicular distance from the focus to the directrix is $2a$ and the coefficient in the standard form $y = Kx^2$ is $|K| = 1/(4a)$.
<p><span class="math-tex">$\frac{\sqrt{5}}{12}$</span></p>
Correct Answer: D