are the vertices of a right triangle, right angled at P, then 
A) \[-2\] or \[4\]
B) \[-2\] or \[-4\]
C) \[2\] or \[-4\]
D) \[2\] or \[2\]
Correct Answer: C
Solution :
| [c] Since, APB is a right triangle, right angles at P. |
| \[\therefore \,\,\,\,\,A{{B}^{2}}=A{{P}^{2}}+B{{P}^{2}}\] |
| \[\Rightarrow \,\,\,{{(11-5)}^{2}}+{{(-5-3)}^{2}}={{(12-5)}^{2}}+{{(y-3)}^{2}}\] |
| \[+{{(12-11)}^{2}}+{{(y+5)}^{2}}\] |
| \[\Rightarrow \,\,\,\,{{6}^{2}}+{{(-8)}^{2}}={{7}^{2}}+{{y}^{2}}-6y+9+1+{{y}^{2}}+10y+25\] \[\Rightarrow \,\,\,\,\,\,2{{y}^{2}}+4y+84=100\] |
| \[\Rightarrow \,\,\,\,\,\,{{y}^{2}}+2y-8=0\] |
| \[\Rightarrow \,\,\,\,\,\,(y+4)\,\,(y-2)=0\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,y=-4\] or 2 |
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