question_answer

Directions: Read the fallowing questions and choose: Statement 1: Condition of orthogonality of two circles \[{{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[{{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\] is \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\].  Statement 2: Angle between the two circles whose distance between the centres is d and radii \[{{r}_{1}},\,{{r}_{2}}\] given by \[\tan \theta =\frac{{{d}^{2}}-r_{1}^{2}-r_{2}^{2}}{2{{r}_{1}}{{r}_{2}}}\]

A)  Both statements are True, Statement-2 explains Statement-1.

B)  Both statements are True, Statement-2 does not explain Statement-1.

C)  Statement-1 is True, Statement-2 is False.

D)  Statement-1 is False, Statement-2 is true.