The equation of the common tangent to the curves y^{2} = 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

The equation of the common tangent to the curves y^{2} = 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

related to an answer for:
The equation of the common tangent to the curves y^2 = 8x and xy = - 1 is

Correct option is (d) y=x+2

Explaination::

tangents to the curve y^{2}=16x is y=mx+4/m , so it must satisfy xy=-4

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

\(mx^2+\frac{4}{m}x+4=0 ,\)

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