The equation of a common tangent to the curves, y2 = 16x and xy = -4 is :

Question

The equation of a common tangent to the curves, y2 = 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

Tardigrade Admin · Accepted Answer

tangent to the parabola y2 = 16 x is y = mx + (4/m) slove it by curve xy = -4 i.e, mx2 + (4/m) x + 4 =0 condition of common tangent is D = 0 ∴ m3 = 1 ⇒ m = 1 ∴ equation of common tangent is y = x + 4

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

$x + y + 4 = 0$

$x - 2 y + 16 = 0$

$2 x - y + 2 = 0$

$x - y + 4 = 0$

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

Q. The equation of a common tangent to the curves, y2=16x and xy=−4 is :

x+y+4=0

x−2y+16=0

2x−y+2=0

x−y+4=0