A) \[\frac{1}{3}\]
B) \[\frac{3}{4}\]
C) \[\frac{4}{3}\]
D) 1
Correct Answer: C
Solution :
Gradients \[\frac{{{m}_{1}}}{{{m}_{2}}}=1:3\] \[{{m}_{1}}=m,\ \ {{m}_{2}}=3m\] \[\therefore {{m}_{1}}+{{m}_{2}}=-\frac{2h}{b}\] .....(i) and \[{{m}_{1}}.{{m}_{2}}=\frac{a}{b}\] .?.(ii) From equation (i), \[m+3m=-\frac{2h}{b}\]or \[m=\frac{-h}{2b}\] From equation (ii), \[m.3m=\frac{a}{b}\] \[3.\frac{{{h}^{2}}}{4{{b}^{2}}}=\frac{a}{b}\Rightarrow \frac{{{h}^{2}}}{ab}=\frac{4}{3}\]. Trick: If the gradients of two lines are in ratio\[1:n\]. Then \[\frac{{{h}^{2}}}{ab}=\frac{{{(n+1)}^{2}}}{4n}=\frac{{{(3+1)}^{2}}}{4.3}=\frac{4}{3}\].
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