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

The equation of the circle which cuts orthogonally the three circles x^(2) + y^(2) + 4x + 2y + 1 = 0 , 2x^(2) + 2y^(2) + 8x + 6y - 3 = 0 , x^(2) + y^(2) + 6x - 2y - 3 = 0 is

Find the equation of the circle which intersects each of the following circles orthogonlly x^2 + y^2 + 4x + 2y + 1 = 0 . 2(x^2 + y^2) + 8x + 6y - 3 = 0, x^2 + y^2 + 6x -2y - 3 =0.

The radical centre of the circles x^(2) + y^(2)- 2x + 6y = 0 , x^(2) + y^(2) - 4x - 2y + 6 = 0 , x^(2) + y^(2) - 12x + 12y + 30 = 0 is

Show that the circles x^2 + y^2 - 2y -8x+ 8 = 0 and x^2 + y^2 - 2x + 6y + 6 = 0 touch each other and find the point of contact.

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

Show that the circles x^(2) + y^(2) + 6x + 2y + 8 = 0 and x^(2) + y^(2) + 2x + 6y + 1 = 0 intersect each other.

2x + y le 6, x + 2y le 8, x ge 0, y ge 0