Question
If, 4x2 + y2 + 12x + 6y + 18 =
0, then find the value of (2x + y)/(y + 6x).Solution
4x2 + y2 + 12x + 6y + 18 = 0
Or, 4x2 + 12x + 9 + y2 + 6y + 9 = 0
Or, (2x) 2 + 2 X (2x) X (3) + 32 + y2 + 2 X y X 3 + 32 = 0
Or, (2x + 3) 2 + (y + 3) 2 = 0 [because, (a + b) 2 = a2 + b2 + 2ab]
The above equation is possible, when,
2x + 3 = 0 and y + 3 = 0
Or, x = - (3/2) = - 1.5 or, y = - 3
So, (2x + y)/(y + 6x) = -6/-12 = 0.5
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