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

Correct option is D.
x-y+4=0
Step 1: Use slope form of tangent equation of parabola
Equation of tangent to parabola y²=4ax in terms of slope 'm' is y=mx+a/m.
Hence, tangent to given parabola y²=16x is y=mx+4/m [Since, a = 4]
Substituting in equation of curve xy=-4 we get mx²+4mx+4=0.. (1)
This is a quadratic equation in terms of x
Step 2: Use condition for equal roots of a quadratic equation
For given line to be tangent to the curve means the line passes through only one point on the curve.
Hence, roots of eqn. (1) must be equal
Hence Discriminant, D=b²-4ac=0
⇒16m²-16m=0
⇒m²=m
⇒m=1
∴Equation of common tangent is y=x+4.
Hence, Option 'D' is correct