A) \[74\]
B) \[62\]
C) \[64\]
D) \[72\]
Correct Answer: D
Solution :
The equation of the line y = x in parametric form is \[\frac{x}{\cos \pi /4}=\frac{y}{\sin \pi /4}\] \[\because \] \[OP=6\sqrt{2}\] \[\therefore \]Coordinates of \[P\] are given by \[\frac{x}{\cos \frac{\pi }{4}}=\frac{y}{\sin \frac{\pi }{4}}=6\sqrt{2}\] \[\Rightarrow \] \[x=y=6\] \[\therefore \]Coordinates of\[P\]are\[(6,\,\,6).\] The equation of circle touching\[y=x\]at\[P\,\,(6,\,\,6)\]is \[{{(x-6)}^{2}}+{{(y-6)}^{2}}+\lambda (x-y)=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}+x(\lambda -12)-y(\lambda +12)+72=0\] Comparing it with\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] \[\lambda -12=2g,\,\,-(\lambda +12=2f\]and\[c=72\] Hence, required value of \[c\] is\[72\].You need to login to perform this action.
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