Question:
<p>The equation of common tangent to the parabolae y<sup>2</sup> = 4x and x<sup>2</sup> = 32y is</p>
<p style="display:inline">x + 2y + 4 = 0</p>
<p style="display:inline">2x - y + 4 = 0</p>
<p style="display:inline">x - 2y + 4 = 0</p>
<p style="display:inline">2x + y + 4 = 0</p>
Step-by-Step Solution
Key Concept: The common tangent to the parabolas y^2=4ax and x^2=4by is found by equating their slope-form tangent conditions, c = a/m and c = -bm^2, to solve for the shared slope m.
<p>Here, a = 1, b = 8<br />
<span class="math-tex">$\therefore$</span> required equation is<br />
<span class="math-tex">$x(1)^{\frac{1}{3}}+y(8)^{\frac{1}{3}}+(8)^{\frac{2}{3}}=0$</span><br />
<span class="math-tex">$\Rightarrow x+y\left(2^{3}\right)^{\frac{1}{3}}+\left(2^{3}\right)^{\frac{2}{3}}=0$</span><br />
<span class="math-tex">$\Rightarrow$</span> x + 2y + 4 = 0</p>
Correct Answer: A