question_answer

If the middle point of a chord of the circle \[{{x}^{2}}+{{y}^{2}}+x-y-1=0\]be (1, 1), then  the length of the chord is 

A)            4    

B)            2

C)            5    

D)            None of these

Correct Answer: D

Solution :

           Here radius of circle is                    \[AC=\sqrt{{{\left( \frac{1}{2} \right)}^{2}}+{{\left( \frac{1}{2} \right)}^{2}}+1}=\sqrt{\frac{3}{2}}\]                    and \[CB=\sqrt{{{\left( \frac{3}{2} \right)}^{2}}+{{\left( \frac{1}{2} \right)}^{2}}}=\sqrt{\frac{10}{4}}=\sqrt{\frac{5}{2}}\]                    Now \[A{{B}^{2}}=A{{C}^{2}}-B{{C}^{2}}=\frac{3}{2}-\frac{5}{2}=-1\]                    \[\Rightarrow \]There is no possible value for AB.                    Aliter : Since the point (1, 1) lies outside the circle, therefore no such chord exist.