Question

The equation of a common tangent to the curves, $y^2 = 16x$ and $xy = -4$ is :

• A. $x + y + 4 = 0$
• B. $x - 2y + 16 = 0$
• C. $2x - y + 2 = 0$
• D. $x - y + 4 = 0$

Answer 1

Answer: (D)

tangent to the parabola $y^2 = 16 x$ is y = mx + $\frac{4}{m}$
slove it by curve xy = -4
$i.e, mx^2 \, + \frac{4}{m} x + 4 =0$
condition of common tangent is D = 0
$\therefore \, \, m^3$ = 1
$\Rightarrow $ $m = 1$
$\therefore $ equation of common tangent is $y = x + 4$