Question

If the line $px+qy=0$ coincides with one of the lines given by $a{x}^2+2hxy+b{y}^2=0$ then

• A. $a{p}^2+2hpq+b{q}^2=0$
• B. $a{q}^2+2hpq+b{p}^2=0$
• C. $a{q}^2-2hpq+b{p}^2=0$
• D. None of these

Answer 1

The correct option is C $a{q}^2-2hpq+b{p}^2=0$

The equation $a{x}^2+2hxy+b{y}^2=0$ can be written as
$a+\frac{2hy}{x}+b(\frac{y}{x}{)}^2=0$...(i)
Consider
$px+qy=0$. or $\frac{y}{x}=\frac{-p}{q}$.
Substituting in equation (i),
$a+2h\left(\frac{-p}{q}\right)+b(\frac{-p}{q}{)}^2=0$
$a{q}^2-2hpq+b{p}^2=0$