The minimum value of p for which the lines 3 x - 4 y = 2 , 3 x - 4 y = 12 , 12 x + 5 y = 7 and 12 x + 5 y = p constitute the sides of a rhombus is

Question

The minimum value of p for which the lines 3 x - 4 y = 2 , 3 x - 4 y = 12 , 12 x + 5 y = 7 and 12 x + 5 y = p constitute the sides of a rhombus is, 33, 19, - 19, 9

MARKS App · Accepted Answer

If the parallelogram is a rhombus, the distance between pair of parallel sides is equal. Hence, 12 - 2 3 2 + 4 2 = ± p - 7 12 2 + 5 2 ⇒ p - 7 = ± 26 ⇒ p = 33 or - 19 Hence, the minimum value of p is - 19

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