The line 5 x + y - 1 = 0 coincides with one of the lines given by 5 x 2 + x y - k x - 2 y + 2 = 0 then the value of k is

Question

The line 5 x + y - 1 = 0 coincides with one of the lines given by 5 x 2 + x y - k x - 2 y + 2 = 0 then the value of k is, - 11, 31, 11, - 31

MARKS App · Accepted Answer

As y 2 is absent in given equation ∴ first line is 5 x + y − 1 = 0 and second is a x + c = 0 ( 5 x + y − 1 ) ( a x + c ) = 0 5 a x 2 + 5 c x + a x y + c y − a x − c = 0 5 a x 2 + a x y + x ( 5 c − a ) + c y − c = 0 Given equation 5 x 2 + x y − k x − 2 y + 2 = 0 ∴ a = 1 ; c = − 2 ∴ − k = 5 c − a − k = 5 ( − 2 ) − 1 − k = − 10 − 1 K = 11

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