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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
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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

by Expert (10.9k points)