Question

The equation of the common tangent to the curves y² = 8x and xy = - 1 is

• (a) 3y = 9x + 2
• (b) y = 2x + 1
• (c) 2y = x + 8
• (d) y = x + 2

Answer 1

Correct option is (d) y=x+2 

Explaination::

tangents to the curve y²=8x is y=mx+2/m , so it must satisfy xy=-1 

\(x({mx+\frac{2}{m}})=-1\) 

\(mx^2+\frac{2}{m}x+1=0 ,\) 

since it has equal roots , therefore D=0

\(\frac{4}{m^2}-4m=0\) 

\(m^3=1 \) 

m=1

therefore , the equation of commom tangent is y=x+2