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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 = ______.
Options
1 : 2
2 : 1
8 : 9
9 : 8
Solution
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`
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