A) 5
B) \[5\sqrt{5}\]
C) 25
D) \[5\sqrt{10}\]
Correct Answer: D
Solution :
Perpendicular bisector of \[A\,(1,\,\,3)\] and \[B\,(-3,\,\,5)\] is \[2x({{x}_{1}}-{{x}_{2}})+2y\,({{y}_{1}}-{{y}_{2}})=(x_{1}^{2}+y_{1}^{2})-(x_{2}^{2}+y_{2}^{2})\] \[\Rightarrow \,\,2x(1+3)+2y(3-5)=(1+9)-(9+25)\] \[\Rightarrow \,\,2x-y+6=0\] .....(i) Perpendicular bisector of \[A\,(1,\,\,3)\] and \[C\,(5,\,\,-1)\] is \[2x\,(1-5)+2y(3+1)=(1+9)-(25+1)\] \[\Rightarrow \,\,x-y-2=0\] .....(ii) Point of intersection of (i) and (ii) is \[P=(-8,\,\,-10)\] Then \[PA=\sqrt{{{(1+8)}^{2}}+{{(3+10)}^{2}}}=\sqrt{81+169}\] \[=\sqrt{250}=5\sqrt{10}\].
You need to login to perform this action.
You will be redirected in
3 sec
