Question

If $4ab = 3h^{2}$, then the ratio of slopes of the lines represented by the equation $ax^{2} + 2hxy + by^{2} = 0$ will be

• A. $\sqrt{2}:1$
• B. $\sqrt{3}:1$
• C. $2:1$
• D. $1:3$

Answer 1

Answer: (D)

$1:3$

Answer 2

Here $m_{1} + m_{2} = \frac{- 2h}{b}$ .....(i) and $m_{1}m_{2} = \frac{a}{b}$ .....(ii)

Also, given that $4ab = 3h^{2}.$ Now we have to find $\frac{m_{1}}{m_{2}}$,

therefore with the help of (i) and (ii), we get

$(m_{1} - m_{2})^{2} = \frac{4h^{2} - 4ab}{b^{2}} = \frac{4h^{2} - 3h^{2}}{b^{2}} = \frac{h^{2}}{b^{2}}$

⇒ $m_{1} - m_{2} = \frac{h}{b}$ .....(iii)

Now on solving (i) and (iii), we get $m_{1} = \frac{- h}{2b}$and $m_{2} = \frac{- 3h}{2b}$

∴$m_{1}:m_{2} = 1:3$.