question_answer

                Statement I: The only circle having radius\[\sqrt{10}\] and a diameter along line is \[{{x}^{2}}+{{y}^{2}}-6x+2y=0.\]                 Statement II:\[2x+y=5\] is a normal to the circle \[{{x}^{2}}+{{y}^{2}}-6x-2y=0.\]     JEE Main Online Paper ( Held On 25  April 2013 )

A)                 Statement I is false; statement II is true.

B)                                        Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.

C)                                        Statement I is true; Statement II is false.

D)                                        Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.

Correct Answer: A

Solution :

                Circle :\[{{x}^{2}}+{{y}^{2}}-6x+2y=0\] Line:\[2x+y=5\] Centre-(3,-1) Now, \[2\times 3-1=5,\]hence centre lies on the given line. Therefore line passes through the centre. The given line is normal to the circle. Thus statement-2 is true, but statement-1 is not true as there are infinite circle according to the given conditions.