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

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+2/m)=-1 mx²+2/mx+1=0, since it has equal roots, therefore D=0 4/m²-4m=0 m³=1 m=1 therefore, the equation of commom tangent is y=x+2

Chapter: Uncategorized· Mathematics

The equation of the common tangent to the curves y^2 = 8x and xy = - 1 is

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

Doubtly Asked 3 Jun 2021 Student doubt jeemain imp jeemain-2019-maths tangents-and-normal Save WhatsApp Report

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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

Doubtly · 3 Jun 2021 Report

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The equation of the common tangent to the curves y^2 = 8x and xy = - 1 is

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