Consider the circle `x^2 + y^2 - 10x - 6y + 30 = 0` Let O be the centre of the circle and tangent at A(7, 3) and passing through A and B,then

Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 6y - 13 = 0 and passing through the centre of the circle x^(2) + y^(2) - 8x - 10y - 8 = 0 .

The normal to-be circle x^2 +y^2 - 4x + 6y -12=0 passes through the point

Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0 . Let B(1,7) and (4,-2) be two points on the circle such that tangents at B and D meet at C. The area of the quadrilateral ABCD is

The number of tangents to the circle x^2 + y^2 - 8x - 6y + 9 = 0 which pass through the point (3, -2) are

Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x-y+4 = 0 and which also passes through the origin.

Let , P be the point on the parabola y^(2) = 8x which is at a minimum distance from the centre C of the circle x^(2) + (y + 6)^(2) =1 . Then the equation of the circle, passing through C and having its centre at P is

Let the equation of an ellipse be (x^(2))/(144) + (y^(2))/(25) = 1 . Then the radius of the circle with centre (0 , sqrt(2)) and passing through the foci of the ellipse is _

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

A circle through the common points of the circles x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) - 2x - 6y + 1 = 0 has its centre on the line 4x - 7y - 19 = 0 . Find the centre and radius of the circle .