Question

if lines represented by equation `px^(2)-qy^(2)=0` are distinct, then
A. `pq gt 0`
B. ` pq lt 0`
C. `pq = 0`
D. ` p +q = 0`

Answer 1

Correct Answer - A
Given pair of line is `px^(2) - qy^(2) = 0 "…"(i)`
On comparing Eq. (i) with `ax^(2) + 2hxy +by^(2) = 0`,
we get `a = p, b = - q, h = 0`
We know that, slopes of `ax^(2) +2hxy + by^(2) = 0`
are real and distinct if and only if `h^(2) - ab gt 0`
`rArr 0 + pq gt0`
`rArr pq gt 0`