Question:
<p>Let <span class="math-tex">\(P Q\)</span> be a chord of the parabola <span class="math-tex">\(y^{2}=12 x\)</span> and the midpoint of PQ be at <span class="math-tex">\((4,1)\)</span>. Then, which of the following point lies on the line passing through the points <span class="math-tex">\(P\)</span> and <span class="math-tex">\(Q\)</span>?</p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{1}{2},-20\right)\)</span></p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{3}{2},-16\right)\)</span></p>
<p style="display:inline"><span class="math-tex">\((3,-3)\)</span></p>
<p style="display:inline"><span class="math-tex">\((2,-9)\)</span></p>
Step-by-Step Solution
Key Concept: The equation of a chord of a parabola with a given midpoint (x1, y1) is determined by the relation T = S1.
<p><img src="https://media-mycbseguide.s3.amazonaws.com/images/question_images/1775195087-yszgy4.jpg" style="height:189px; width:200px" /><br />
<span class="math-tex">\(T=S_{1}\)</span><br />
<span class="math-tex">\(y-6(x+4)=1-48\)</span><br />
<span class="math-tex">\(\Rightarrow 6 x-y=23\)</span><br />
<span class="math-tex">\(\left(\frac{1}{2},-20\right)\)</span> will satisfy the equation <span class="math-tex">\(6 x-y =23\)</span></p>
Correct Answer: A