The Equation Of The Common Tangent To The Curves y2 = 8x and xy = –1 Is

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Question

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

Solution

Correct option is

y = x + 2

Any tangent to y2 = 8x(a = 2) is . If it is a tangent to xy = –1, then it will cut the hyperbola in two coincident points.

     Δ = 0 i.e., 4 – 4m2 = 0   

Hence y = x + 2 is the common tangent.

SIMILAR QUESTIONS

Q1

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Q2

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Q3

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Q4

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Q5

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Q6

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Q7

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Q8

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Q9

 

The equation of the common tangent touching the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis is

Q10

A tangent and a normal are drawn at the point P(16, 16) of the parabola y2 = 16x which cut the axis of the parabola at the points A and B respectively. If the center of the circle through P, A and B is C, then angle between PC and axis of x is