Question

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

• (a) x-y+4=0
• (b) x+y+4=0
• (c) x-2y+16=0
• (d) 2x-y+2=0

Answer 1

Correct option is (d) y=x+2 

Explaination::

tangents to the curve y²=16x is y=mx+4/m , so it must satisfy xy=-4 

$x(mx+\frac{4}{m})=-4$

$m{x}^2+\frac{4}{m}x+4=0,$

since it has equal roots , therefore D=0

$\frac{16}{m^2}-16m=0$

$m^3=1$

m=1

therefore , the equation of commom tangent is  y=x+4 i.e. x-y+4=0