Show that for the circle `x^(2)+y^(2)-8x-10y+7=0` centre is (4,5) and radius = sqrt(34)`

The y-intercept of the circle x^(2)+y^(2)+4x+8y-5=0 is

Find the equations of the two tangents to the circle x^(2) +y^(2)- 8x - 10y - 8 = 0 which are perpendicular to the line 5x - 12y = 2.

To the circle x^(2)+y^(2)+8x-4y+4=0 tangent at the point theta=(pi)/4 is

Find the equation of the circle which passes through the centre of the circle x^(2)+y^(2)+8x+10y-7=0 and is concentric with the circle 2x^(2)+2y^(2)-8x-12y-9=0

The least distance between two points P and Q on the circle x^(2) + y^(2) -8x + 10y + 37 =0 and x^(2) + y^(2) + 16x + 55 = 0 is _______ .

If the circle x^(2) + y^(2) -4x - 8y + 16 =0 rolls up the tangent to it at (2 + sqrt(3), 3) by 2 units (assumes x-axis as horizontal), then the centre of the circle in the new position is

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.

Equation of the circle concentric with the circle x^(2) + y^(2) + 8x + 10 y - 7 = 0 , and passing through the centre of the circle x^(2) + y^(2) - 4x - 6y = 0 ,is

A circle of radius 2 units rolls inside the ring of the circle x^(2)+y^(2)+8x-2y-19=0 then the locus of its centre is

If the radius of the circle touching the pair of lines 7x^(2) - 18 xy +7y^(2) = 0 and the circle x^(2) +y^(2) - 8x - 8y = 0 , and contained in the given circle is equal to k, then k^(2) is equal to