Question

If $y = mx + 4$ is a tangent to both the parabolas, $y^2 = 4x$ and $x^2 = 2by$, then b is equal to :

• A. -64
• B. 128
• C. -128
• D. -32

Answer 1

Answer: (C)

$y = mx + 4$ is tangent to $y^2 = 4x$
$\Rightarrow m = \frac{1}{4}$
$y = \frac{1}{4} x+4$ is tangent to $x^{2} = 2by$
$\Rightarrow x^{2} - \frac{b}{2}x-8b = 0$
$\Rightarrow D = 0$
$b^{2} + 128b = 0$
$\Rightarrow b = - 128, 0$
$b\ne 0 \Rightarrow b = -128$