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Maths-

General

Easy

Question

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

3y = 9x + 2
y = 2x + 1
2y = x + 8
y = x + 2

The correct answer is: y = x + 2

Any tangent is y = mx + $fraction numerator a over denominator m end fraction$ $rightwards double arrow$ y = mx + $fraction numerator 2 over denominator m end fraction$ . If it is tangent to xy = –1 then it will cut at two coincident points.
$therefore$ x $open parentheses m x plus fraction numerator 2 over denominator m end fraction close parentheses$ + 1 = 0 $rightwards double arrow$ m²x² + 2x + m = 0
Δ = 0 ; 4 – 4m³ = 0 $rightwards double arrow$ m = 1 so y = x + 2

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physics-General

parallel

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