A) \[{{b}^{2}}=2{{a}^{2}}\]
B) \[b={{a}^{2}}\]
C) \[{{a}^{2}}=2{{b}^{2}}\]
D) \[a=b\]
E) \[a=-b\]
Correct Answer: C
Solution :
Given, points are\[P(0,b),Q(0,0)\]and\[R(a,0)\]. Then, coordinates of \[M=\left( \frac{0+a}{2},\frac{0+0}{2} \right)=\left( \frac{a}{2},0 \right)\] And \[N=\left( \frac{0+a}{2},\frac{b+0}{2} \right)=\left( \frac{a}{2},\frac{b}{2} \right)\] Slope of\[PM=\frac{0-b}{a/2-0}\]or\[\frac{-2b}{a}={{m}_{1}}\](say) Slope of\[QN=\frac{b/2-0}{a/2-0}\] \[\Rightarrow \] \[\frac{b}{a}={{m}_{2}}\] (say) Given, \[PM\bot QN\] \[\Rightarrow \] \[{{m}_{1}}.{{m}_{2}}=-1\] \[\Rightarrow \] \[\frac{+2b}{a}.\frac{b}{a}=-1\] \[\Rightarrow \] \[{{a}^{2}}=2{{b}^{2}}\]You need to login to perform this action.
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