Question:
<p>Find the equation of directrix of parabola y<sup>2</sup>=100x.</p>
<p style="display:inline"><span class="math-tex">\(y=25\)</span></p>
<p style="display:inline"><span class="math-tex">\(x=25\)</span></p>
<p style="display:inline"><span class="math-tex">\(x=-25\)</span></p>
<p style="display:inline"><span class="math-tex">\(y=-25\)</span></p>
Step-by-Step Solution
Key Concept: Identify the parameter $a$ by comparing the given equation with the standard form $y^2 = 4ax$ to apply the directrix formula $x = -a$.
<p><span class="math-tex">$x=-25$</span><br />
Comparing equation with <span class="math-tex">${y}^2=4 a {x}$</span>.<br />
<span class="math-tex">$4 a=100=>a=25$</span>. Directrix is a line parallel to latus rectum in such a way that vertex is at middle of both.<br />
Equation of directrix is <span class="math-tex">$x=-a=>x=-25$</span>.</p>
Correct Answer: C