Prove that a circle cutting the circle `x^2 + y^2=4` orthogonally and having its centre on the line `2x-2y+9=0`, passes through two fixed points. Also find the points.

Find the equation of the circle which cuts the circle x^(2)+y^(2)+5x+7y-4=0 orthogonally, has its centre on the line x=2 and passes through the point (4,-1).

The centre of the circle S=0 lie on the line 2x – 2y +9=0 & S=0 cuts orthogonally x^2 + y^2=4 . Show that circle S=0 passes through two fixed points & find their coordinates.

If centre of a circle lies on the line 2x - 6y + 9 =0 and it cuts the circle x^(2) + y^(2) = 2 orthogonally then the circle passes through two fixed points

Find the equation of the circle which has its centre on the line y = 2 and which passes through the points (2,0) and (4,0).

Find the general equation of a circle cutting x^2 + y^2=c^2 orthogonally and show that if it passes through the point (a, b) , it will also pass through the point. ((c^2 a)/(a^2 + b^2) , (c^2 b)/(a^2+b^2)) .

A variable circle which always touches the line x+y-2=0 at (1, 1) cuts the circle x^2+y^2+4x+5y-6=0 . Prove that all the common chords of intersection pass through a fixed point. Find that points.

Find the equation of the circle which cuts orthogonally the circle x^2+y^2-4x+2y-7=0 and having the centre at (2,3)

Prove that the line x(a+2b) + y (a-3b)=a-b passes through a fixed point for different values of a and b . Also find the fixed point.

A circle whose centre is the point of intersection of the lines 2x-3y+4=0\ a n d\ 3x+4y-5=0 passes through the origin. Find its equation.

If a circle Passes through a point (1,0) and cut the circle x^2+y^2 = 4 orthogonally,Then the locus of its centre is