Question

If $\frac{x^2}{a}+\frac{y^2}{b}+\frac{2xy}{h}=0$ represent pair of straight lines and slope of one line is twice the other. Then $ab:h^2$ is

• A. $9:8$
• B. $8:9$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is A $9:8$

Given,

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

represent pair of straight lines and slope of one line is twice the other

Let,

$y=mx,y=2mx$

$(y-mx)(y-2mx)=0$

upon solving the above equation, we get,

$2m^2{x}^2-3mxy+y^2=0$.......(2)

comparing (1) and (2), we get,

$2m^2=\frac{1}{a}\Rightarrow a=\frac{1}{2m^2}$

$1=\frac{1}{b}\Rightarrow b=1$

$-3m=\frac{2}{h}\Rightarrow h=-\frac{2}{3m}$

$ab:h^2=\frac{1}{2m^2}\times 1:{(-\frac{2}{3m})}^2$

$=\frac{1}{2m^2}:\frac{4}{9m^2}$

$=9:8$