Question

If one of the lines represented by the equation $a{x}^2+2hxy+b{y}^2=0$ be $y=mx$, then

• A. $b{m}^2+2hm+a=0$
• B. $b{m}^2+2hm–a=0$
• C. $a{m}^2+2hm+b=0$
• D. $a{m}^2-2hm+b=0$

Answer 1

The correct option is A

$b{m}^2+2hm+a=0$

Explanation for the correct solution

We know that $y=mx$ is one of the lines that is represented by $a{x}^2+2hxy+b{y}^2=0$.

Then, if we put $y=mx$ in the equation $a{x}^2+2hxy+b{y}^2=0$ then the equation will be satisfied.

$\begin{array}{rcl}\therefore a{x}^2+2hxy+b{y}^2& =& a{x}^2+2hx\left(mx\right)+b{\left(mx\right)}^2\\ & =& a{x}^2+2hm{x}^2+b{m}^2{x}^2\\ & =& x^2\left(a+2hm+b{m}^2\right)\end{array}$

From this, one can conclude that $a+2hm+b{m}^2=0$.

Hence, the correct option is (A).