If the slope of one of the lines given by a x 2 + 2 h x y + b y 2 = 0 is two times the other then

Question

If the slope of one of the lines given by a x 2 + 2 h x y + b y 2 = 0 is two times the other then, 8 h 2 = 9 a b, 8 h 2 = 9 a b 2, 8 h = 9 a b, 8 h = 9 a b 2

MARKS App · Accepted Answer

a x 2 + 2 h x y + b y 2 = 0 m 1 + m 2 = − 2 h b ...... ( 1 ) m 1 . m 2 = a b ...... ( 2 ) m 1 = 2 m 2 ...... ( 3 ) Put (3) in (1) 3 m 2 = − 2 h b m 2 = − 2 h 3 b Put (3) in (2) 2 m 2 . m 2 = a b 2 ( m 2 ) 2 = a b ∴ 2 ( − 2 h 3 b ) 2 = a b ∴ 8 h 2 = 9 a b .

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