Question

If the pair of lines $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the y-axis then

• A. $2fgh = bg^2 + ch^2$
• B. $bg^2 \neq ch^2$
• C. $abc = 2fgh$
• D. none of these

Answer 1

Answer: (A)

Put x = 0 in the given equation
$\Rightarrow \, by^2 + 2 fy + c = 0$.
For unique point of intersection $f^2- bc = 0 $
$ \Rightarrow \, af^2 - abc = 0$.
Since $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$
$ \Rightarrow \, 2fgh - bg^2 - ch^2 = 0$