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If the line y = m x + c touches the parabola y 2 = 12 x + 3 exactly for one value of m m > 0 , then the value of c + m c - m is equal to

Correct answer

1.4

Step-by-step solution

Equation of the tangent to y 2 = 12 x + 3 with slope m is y = m x + 3 + 3 m , which is same as y = m x + c ⇒ c = 3 m + 3 m ⇒ 3 m 2 - m c + 3 = 0 which is quadratic in ‘ m ’ Since, it has both roots equal ⇒ c 2 - 36 = 0 ⇒ c = ± 6 ⇒ c = 6   m > 0 ⇒ c > 0 ⇒ m = 1   &   c = 6 ⇒ c + m c - m = 7 5 = 1 . 4

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