A) \[\frac{ab}{3}\]
B) \[\frac{4ab}{3}\]
C) \[\frac{4a}{3b}\]
D) None of these
Correct Answer: B
Solution :
Let \[y={{m}_{1}}x\] and \[y={{m}_{2}}x\] be the lines represented by the given equation. Then, \[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\]and\[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] We have, \[{{m}_{1}}:{{m}_{2}}=3:1\] \[\Rightarrow \] \[{{m}_{1}}=3{{m}_{2}}\] \[\because \] \[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\]and\[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] \[\therefore \] \[4{{m}_{2}}=-\frac{2h}{b}\]and\[3m_{2}^{2}=\frac{a}{b}\] On solving above equations, we get \[3{{\left( -\frac{h}{2b} \right)}^{2}}=\frac{a}{b}\] \[\Rightarrow \] \[{{h}^{2}}=\frac{4ab}{3}\]
You need to login to perform this action.
You will be redirected in
3 sec
