question_answer

The equation of the circle passing through the point (2, 1) and touching y-axis at the origin is

A)            \[{{x}^{2}}+{{y}^{2}}-5x=0\]                                          

B)            \[2{{x}^{2}}+2{{y}^{2}}-5x=0\]

C)            \[{{x}^{2}}+{{y}^{2}}+5x=0\]                                        

D)            None of these

Correct Answer: B

Solution :

           We have the equation of circle                    \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]                    But it passes through (0, 0) and (2, 1), then                                    \[c=0\]                                               ?.(i)                    \[5+4g+2f=0\]                                                ?.(ii)                    Also \[\sqrt{{{g}^{2}}+{{f}^{2}}-c}=\ |g|\] Þ \[f=0\]     \[\{\because \ c=0\}\]                    From (ii), \[g=-\frac{5}{4}\]                    Hence the equation will be\[2{{x}^{2}}+2{{y}^{2}}-5x=0\].