A) \[{{(x+y)}^{2}}=9\]
B) \[{{x}^{2}}+{{(3-x)}^{2}}=9\]
C) \[xy=0\]
D) \[{{(3-x)}^{2}}+{{y}^{2}}=9\]
Correct Answer: C
Solution :
Given, \[{{x}^{2}}+{{y}^{2}}=9\] .....(i) \[x+y=3\] .....(ii) From equation (i) and (ii), we find the point of intersection. Now, \[{{x}^{2}}+{{(x-3)}^{2}}=9\Rightarrow {{x}^{2}}+9+{{x}^{2}}-6x=9\] \[\Rightarrow 2{{x}^{2}}=6x\Rightarrow x=3\] Putting \[x=3\] in equation (ii), \[y=0\] Similarly to get second point Putting \[x=3-y\] in equation (i) \[y=3,\,x=0\]. So, the co-ordinates of both points are \[(3,\,0)\] and \[(0,\,3)\]. So, separate equation of lines joining these points from origin \[y-0=\frac{0-0}{0-3}\,(x-3)\Rightarrow y=0\]. Now, taking point (0, 0) and (0, 3) we get \[x=0\] Hence, required equation of pair of lines is \[xy=0\].
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