120002 Find the value of \(m+n\), if the circumference of the circle \(x^2+y^2+8 x+8 y-m=0\) is bisected by the circle \(x^2+y^2-2 x+4 y+n=0\).

120003 The point on the circle \(x^2+y^2=4\) whose distance from the line \(4 x+3 y-12=0\) is \(4 / 5\) units is equal to

120006 If one of the two circle
\(x^2+y^2+\alpha_1(x-y)+c=0\) and
\(x^2+y^2+\alpha_2(x-y)+c=0\), lies within the
other, then \(\qquad\) (where \(\alpha_1, \alpha_2 \in \mathbf{R}, \alpha_1 \neq \alpha_2\) )

120007 The length of the chord intercepted by the circle \(x^2+y^2-6 x+8 y-5=0\) on the line \(2 x-y\) \(=5\) is equal to ..... units

120002 Find the value of \(m+n\), if the circumference of the circle \(x^2+y^2+8 x+8 y-m=0\) is bisected by the circle \(x^2+y^2-2 x+4 y+n=0\).

120003 The point on the circle \(x^2+y^2=4\) whose distance from the line \(4 x+3 y-12=0\) is \(4 / 5\) units is equal to

120006 If one of the two circle
\(x^2+y^2+\alpha_1(x-y)+c=0\) and
\(x^2+y^2+\alpha_2(x-y)+c=0\), lies within the
other, then \(\qquad\) (where \(\alpha_1, \alpha_2 \in \mathbf{R}, \alpha_1 \neq \alpha_2\) )

120007 The length of the chord intercepted by the circle \(x^2+y^2-6 x+8 y-5=0\) on the line \(2 x-y\) \(=5\) is equal to ..... units

120002 Find the value of \(m+n\), if the circumference of the circle \(x^2+y^2+8 x+8 y-m=0\) is bisected by the circle \(x^2+y^2-2 x+4 y+n=0\).

120003 The point on the circle \(x^2+y^2=4\) whose distance from the line \(4 x+3 y-12=0\) is \(4 / 5\) units is equal to

120006 If one of the two circle
\(x^2+y^2+\alpha_1(x-y)+c=0\) and
\(x^2+y^2+\alpha_2(x-y)+c=0\), lies within the
other, then \(\qquad\) (where \(\alpha_1, \alpha_2 \in \mathbf{R}, \alpha_1 \neq \alpha_2\) )

120007 The length of the chord intercepted by the circle \(x^2+y^2-6 x+8 y-5=0\) on the line \(2 x-y\) \(=5\) is equal to ..... units

120002 Find the value of \(m+n\), if the circumference of the circle \(x^2+y^2+8 x+8 y-m=0\) is bisected by the circle \(x^2+y^2-2 x+4 y+n=0\).

120003 The point on the circle \(x^2+y^2=4\) whose distance from the line \(4 x+3 y-12=0\) is \(4 / 5\) units is equal to

120006 If one of the two circle
\(x^2+y^2+\alpha_1(x-y)+c=0\) and
\(x^2+y^2+\alpha_2(x-y)+c=0\), lies within the
other, then \(\qquad\) (where \(\alpha_1, \alpha_2 \in \mathbf{R}, \alpha_1 \neq \alpha_2\) )

120007 The length of the chord intercepted by the circle \(x^2+y^2-6 x+8 y-5=0\) on the line \(2 x-y\) \(=5\) is equal to ..... units