If the circles x^2 + y^2 - 2ax + c = 0 and x^ | vedclass

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(D) The general equation of a circle is $x^2 + y^2 + 2gx + 2fy + c = 0$.For the first circle $x^2 + y^2 - 2ax + c = 0$,we have $g_1 = -a$,$f_1 = 0$,an

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None of these

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(D) The general equation of a circle is $x^2 + y^2 + 2gx + 2fy + c = 0$.For the first circle $x^2 + y^2 - 2ax + c = 0$,we have $g_1 = -a$,$f_1 = 0$,and $c_1 = c$.For the second circle $x^2 + y^2 + 2by + 2\lambda = 0$,we have $g_2 = 0$,$f_2 = b$,and $c_2 = 2\lambda$.The condition for two circles to intersect orthogonally is $2(g_1g_2 + f_1f_2) = c_1 + c_2$.Substituting the values,we get $2((-a)(0) + (0)(b)) = c + 2\lambda$.$0 = c + 2\lambda$.Therefore,$2\lambda = -c$,which implies $\lambda = -\frac{c}{2}$.Since $-\frac{c}{2}$ is not among the options $A, B, C$,the correct choice is $D$.

If the circles $x^2 + y^2 - 2ax + c = 0$ and $x^2 + y^2 + 2by + 2\lambda = 0$ intersect orthogonally,then the value of $\lambda$ is

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