The gradient of one of the straight line in ax^2+2hxy+by^2= 0 is twice that of the other.Then which one of the following is true? (i) 8h^2+9ab=0 (ii)8h^2=9ab (iii)h^2=ab (iv) 3h^2-5ab=0

Alex Baird 2022-07-30 Answered
The gradient of one of the straight line in a x 2 + 2 h x y + b y 2 = 0 is twice that of the other.Then which one of the following is true?
( i ) 8 h 2 + 9 a b = 0   ( i i ) 8 h 2 = 9 a b
( i i i ) h 2 = a b   ( i v ) 3 h 2 5 a b = 0
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Answers (1)

renegadeo41u
Answered 2022-07-31 Author has 9 answers
if m 1 & m 2 are 2 slopes for the pairof straight lines a x 2 + 2 h x y + b y 2 = 0 then
m 1 + m 2 = 2 h / b   &   m 1 m 2 = a / b
but m 2 = 2 m 1
3 m 1 = 2 h / b   &   2 m 1 m 1 = a / b........(1)
m 1 = 2 h / 3 b
sub. m 1 in (1) we get 2 ( 4 h 2 / 9 b 2 ) = a / b
8 h 2 = 9 a b
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