Question

If `x^2/a + y^2/b + (2xy)/h` = 0 represents a pair of lines and slope of one line is twice the other, then find the value of ab : h².

Answer 1

`x^2/a + y^2/b + (2xy)/h` = 0

∴ bhx² + ahy² + 2abxy = 0

Let slope of lines be m and 2m.

∴ m + 2m = `-(2ab)/(ah)`

∴ 3m = `-(2b)/h`   ....(1)

and (m)(2m) = `(bh)/(ah) = b/a`

∴ 2m² = `b/a`

Using (1):

`2((-2b)/(3h))^2 = b/a`

∴ `(8b^2)/(9h^2) = b/a`

∴ 8ab = 9h²

∴ `(ab)/h^2 = 9/8`