A) Both I and II
B) Neither I nor II
C) Only I
D) Only II
Correct Answer: B
Solution :
I. We have the equation of circle \[{{x}^{2}}+{{y}^{2}}-6x-4y-7=0\] Here,\[g=-3,\]\[f=-2,\] \[c=-7\] Condition that the circle touches y-axis is \[{{f}^{2}}=c\] But for the given circle, this condition does not follow, since \[{{f}^{2}}\ne c\] \[[\because \,{{(-2)}^{2}}\ne -7]\] Hence, the circle does not touch y-axis. II. The equation of circle is \[{{x}^{2}}+{{y}^{2}}+6x+4y-7=0\] Here, \[g=3,\,f=2,\,c=-7\] We know, the condition that the circle touches \[x-\]axis is \[{{g}^{2}}=c\] But for the given circle, this condition does not follow, since \[{{g}^{2}}\ne c\] \[[\because \,({{3}^{2}})\ne -7]\] Hence, the circle does not touch \[x-\]axis.
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