A circle of equation `x^2+y^2+ax+by+c=0` passes through `(0,6)` and touches `y=x^2` at `(2,4)` then find the value of `a+c`

If a circle passes through (0,0),(4,0) and touches the circle x^(2)+y^(2)=36 then the centre of circle

Centre of a circle passing through point (0,1) and touching the curve y=x^2 at (2,4) is

A circle passes through (0,0) and (1,0) and touches the circle x^(2)+y^(2)=9 then the centre of circle is -

If the radical axis of the circles x^(2)+y^(2)-6x-8y+c=0 and x^(2)+y^(2)-8x-6y+c=0 passes through (-1,1) then find the value of c

Find the equation of the circle which cuts orthogonally the circle x^(2)+y^(2)6x+4y-3=0, passes through (3,0) and touches the axis of y.

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the line y = x touches it at the origin, then