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The equation of the common tangent to the curves y 2 = 4 x and x 2 + 32 y = 0 is x + b y + c = 0 . The value of | sin – 1 ( sin   1 ) + sin – 1 ( sin   b ) + sin – 1 ( sin   c ) | is equal to

Correct answer

1

Step-by-step solution

y = mx + 1 m is tangent to y 2 = 4 x Now, x 2 + 32 mx + 1 m = 0 ⇒ x 2 + 3 2 mx + 3 2 m = 0 ⇒ 3 2 m 2 - 4 × 3 2 m = 0 ⇒ m = 1 2 Equation of the tangent is x – 2 y + 4 = 0 ⇒ | sin - 1 ( sin 1 ) + sin - 1 ( sin ( - 2 ) ) + sin - 1 ( sin 4 ) | = | 1 + 2 – π + π – 4 | = 1

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