Question

The slope of one of the lines given by $a{x}^2+2hxy+b{y}^2=0$ is $k$ times the other, then

• A. $4k^{2}h=ab(1+k)$
• B. $k{h}^2=4ab(1+k{)}^2$
• C. $k{h}^2=2ab(1+k{)}^2$
• D. $4k{h}^2=ab(1+k{)}^2$

Answer 1

The correct option is A $4k^{2}h=ab(1+k)$

$a{x}^2+2hxy+b{y}^2=0$

$a\left(1\right)+2h\left(\frac{y}{x}\right)++b{\left(\frac{y}{x}\right)}^2=0$

$a+2h\left(m\right)+b{m}^2=0$ .... $m_1$ ........... $m_2$

$m_1+m_2=-2h/b$ $m_1=k{m}_2$

$m_1{m}_2=a/b$

$m^2=\frac{a}{bk}\Rightarrow m=\sqrt{\frac{a}{bk}}$

$4k^{2}h=ab(1+k)$