`{:(y = 2x - 6),(y = 0):}`

Find the equation of the circle whose radius 4 and which is concentric with the circle x ^2 + y ^2 + 2x - 6y = 0.

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

Find the internal centre of similitude for the circles x^(2) + y^(2) + 6x - 2y + 1 =0 and x^(2) + y^(2) - 2x - 6y + 9 = 0 .

If the circle x^2+y^2+6x+8y+a=0 bisects the circumference of the circle x^2 + y^2 + 2x - 6y - b = 0 then (a + b) is equal to

Find the equation of the circle which passes through the points of intersection of circles x^2 + y^2 - 2x - 6y + 6 = 0 and x^2 + y^2 + 2x – 6y + 6 = 0 and intersects the circle x^2 + y^2 + 4x + 6y +4=0 orthogonally.

The point (1,2) lies inside the circle x^(2) + y^(2) - 2x + 6y + 1 = 0 .

x - 2y + 2 = 0, 2x + y - 6= 0

The circles x^2 + y^2 + 6x + 6y = 0 and x^2 + y^2 - 12x - 12y = 0

Show that the circles x^(2) + y^(2) + 2 x -6 y + 9 = 0 and x^(2) +y^(2) + 8x - 6y + 9 = 0 touch internally.