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Let C 1 be the graph of x y = 1 and the reflection of C 1 in the line y = 2 x is C 2 . If the equation of C 2 is expressed as 12 x 2 + b x y + c y 2 + d = 0 , then the value of ( b + c + d ) is equal to

Correct answer

6

Step-by-step solution

Any point on the hyperbola x y = 1 is t , 1 t Now, the image of t , 1 t by the line mirror y = 2 x is x - t 2 = y - 1 t - 1 = - 2 2 t - 1 t 5 ⇒ 5 x = 4 t - 3 t and 5 y = 4 t + 3 t Now eliminating t from above two equations we get, 12 x 2 - 12 y 2 - 7 x y + 25 = 0 ∴ b + c + d = 6

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