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The equation to the pair of lines parallel to 2x2+4xy+y2=0 and passing through 1,2 is 2x2+4xy+y2+kx8y+14=0 then  k=  

a
-8
b
-11
c
-12
d
8

detailed solution

Correct option is C

The combined equation of pair of lines passing through the point x1,y1and parallel to the pair of lines ax2+2hxy+by2=0 is ax−x12+2hx−x1y−y1+by−y12=0Hence, the required equation is 2x−12+4x−1y−2+2y−22=0Simplify,2x−12+4x−1y−2+y−22=02x2−4x+2+4xy−8x−4y+8+y2−4y+4=02x2+4xy+y2−12x−8y+14=0The coefficient of x in the above equation is k=−12

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