Question:
<p>The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y<sup>2</sup> = 8x is</p>
<p style="display:inline"><span class="math-tex">\(2 \sqrt{41}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\sqrt{41}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{3}{2} \sqrt{41}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{1}{2} \sqrt{41}\)</span></p>
Step-by-Step Solution
Key Concept: The chord of contact from an external point (x₁, y₁) to parabola y² = 4ax has equation yy₁ = 2a(x + x₁). The length formula is L = (1/2)√[(y₁² - 4ax₁)(y₁² + 4a²)], where the two endpoints satisfy both the parabola equation and the chord of contact equation.
<p>Here, a = 2, x<sub>1</sub> = 2, y<sub>1</sub> =5<br />
The length of the chord<br />
<span class="math-tex">$=\frac{1}{2} \sqrt{[25-4(2)(2)]\left[25+4(2)^{2}\right]}$</span><br />
<span class="math-tex">$=\frac{3}{2} \sqrt{41}$</span></p>
Correct Answer: C