question_answer

The equation of the circle which touches x-axis at (3, 0) and passes through (1, 4) is given by                                 [MP PET 1993]

A)            \[{{x}^{2}}+{{y}^{2}}-6x-5y+9=0\]

B)            \[{{x}^{2}}+{{y}^{2}}+6x+5y-9=0\]

C)            \[{{x}^{2}}+{{y}^{2}}-6x+5y-9=0\]

D)            \[{{x}^{2}}+{{y}^{2}}+6x-5y+9=0\]

Correct Answer: A

Solution :

           \[{{k}^{2}}=4+{{(k-4)}^{2}}\Rightarrow k=\frac{5}{2}\]                    Hence required equation of circle is               \[{{(x-3)}^{2}}+{{\left( y-\frac{5}{2} \right)}^{2}}={{\left( \frac{5}{2} \right)}^{2}}\Rightarrow {{x}^{2}}+{{y}^{2}}-6x-5y+9=0\] Trick: Only (a) passes through (1, 4).