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if X^2/a+y^2/b+(2xy)/h=0 represent pair ...

if `X^2/a+y^2/b+(2xy)/h=0` represent pair of straight lies and slope one line is twice the other line then `ab:h^2`.

A

`9:8`

B

`8:9`

C

`1:2`

D

`2:`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `(1)/(a)x^2+(1)/(b)y^2+2(1)/(h)xy=0`
`therefore m_1+m_2=-(2//h)/(1//b)=(-2b)/(h)` .......(i)
and `m_1m_2=(1//a)/(a//b)=(b)/(a)` ......(ii)
Also , given , `m_2=2m_1`
`rArr 3m_1=(-2b)/(h)` ....(iii)
and `2m_(1)^(2)=(b)/(a)` ......(iv)
From Eqs.(iii) and (iv), we get
`(9m_(1)^(2))/(2m_(1)^(2))=(4b^2)/(h^2)xx(a)/(b)`
`rArr (9)/(8)=(ba)/(h^2)rArr ab:h^2=9:8`
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