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

Question

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

Accepted Answer

Let the equation of tangent to parabola

y2 = 16x is y = mx + $${4 \over m}$$    ...... (1)

It is given that tangent to xy = -4 .........(2)

Solving (1) and (2) we get

$$x\left( {mx + {4 \over m}} \right) + 4 = 0$$

$$ \Rightarrow m{x^2} + {4 \over m}x + 4 = 0$$

Now for tangent D = 0 $$ \Rightarrow {{16} \over {{m^2}}} - 16m = 0$$

$$ \Rightarrow {m^3} = 1$$ $$ \Rightarrow $$ m = 1

Now putting value of m in Equation (1)

y = x + 4 or x -- y + 4 = 0

Solutions · 1