A) \[{{\left( x-1 \right)}^{2}}+{{y}^{2}}=5\]
B) \[{{x}^{2}}+{{\left( y-1 \right)}^{2}}=25\]
C) \[{{(x-1)}^{2}}+{{\left( y-1 \right)}^{2}}=5\]
D) \[{{x}^{2}}+{{y}^{2}}=25\]
Correct Answer: A
Solution :
Mirror image of A \[(4,-1)\] with espect to line \[x-1=0\] and \[x-y-1=0\] ire respectively \[(-2,-1)\] and (0, 3) which lie on BC |
Equation of \[BC=2x-y+3=0\] |
\[r=\left| \frac{2-0+3}{\sqrt{5}} \right|=\frac{5}{\sqrt{5}}=\sqrt{5}\] |
Now image of D, E , F are also lies on circumcircle with respect to the diameter. |
\[\therefore \] D', E', F' are lie on in circle of \[\Delta ABC\] |
Equation of in circle of |
\[\Delta ABC={{\left( x-1 \right)}^{2}}+{{y}^{2}}=5\] |
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