Question

If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h² = ______.

विकल्प

• 1 : 2

• 2 : 1

• 8 : 9

• 9 : 8

Answer 1

If the slope of one of the two lines given by `"x"^2/"a" + "2xy"/"h" + "y"^2/"b" = 0` is twice that of the other, then ab : h² = 9 : 8.

Explanation:

ax² + 2hxy + by² =0

m₁ + m₂ = `(-2"h")/"b"` and m₁m₂ = `"a"/"b"`

where m₁ = Km₂ 

Km₁ + m₂ = `(-2"h")/"b"`

m₂(K+1) =`(-2h)/(b)` 

m₂ = `(-2h)/(b(K+1))` 

Km₂m₂ = `a/b`

`"K" "m"_2^2 = a/b`

`"K" ((-2h)/(b(K+1)))^2 = a/b`

`K (4h^2)/(b^2(K+1)^2) = a/b`

`4Kh^2 = (K+1)^2ab`

`4(2)(1/h)^2 = 9 1/a 1/b`

`8/h^2 =9/(ab)`

`(ab)/h^2=9/8`