If 9x^2-24 xy+16y^2+ αx+ βy+6 represents a pair of parallel lines of 1 unit apart and one of those lines passes through (1 ,1 ), then is equal to

Question

Accepted Answer

Correct answer: D. (d) Given 9x^2-24 xy+16y^2+ αx+ βy+6=0 On comparing with ax^2+2 hxy+by^2+2 gx+2 fy+c=0a=9 ,b=16 ,c=6h=-12 ,g= 2 ,f= 2 Hence, given equation will represent pair of parallel lines, if h^2= ab and af^2=bg^2 Now, we have = 34

$If 9 x^{2} - 24 xy + 16 y^{2} + αx + βy + 6 represents a pair of parallel lines of 1 unit apart and one of those lines passes through (1, 1), then \frac{α}{β} is equal to$

Solution

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