A circle passes through the origin and has its center on `y=x` If it cuts `x^2+y^2-4x-6y+10=-` orthogonally, then find the equation of the circle.

If a circle passes through the point (a, b) and cuts the circle x^2 +y^2=k^2 orthogonally, then the equation of the locus of its center is

Find the range of parameter a for which a unique circle will pass through the points of intersection of the hyperbola x^2-y^2=a^2 and the parabola y=x^2dot Also, find the equation of the circle.

Find the range of parameter a for which a unique circle will pass through the points of intersection of the hyperbola x^2-y^2=a^2 and the parabola y=x^2dot Also, find the equation of the circle.

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

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at Aa n dB , then find the equation of the circle on A B as diameter.

If the two circles 2x^2+2y^2-3x+6y+k=0 and x^2+y^2-4x+10 y+16=0 cut orthogonally, then find the value of k .

lf a circle C passing through (4,0) touches the circle x^2 + y^2 + 4x-6y-12 = 0 externally at a point (1, -1), then the radius of the circle C is :-

If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 as its asymptotes, then find the equation of its transvers and conjugate axes.

If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 as its asymptotes, then find the equation of its transvers and conjugate axes.

consider a family of circles passing through two fixed points S(3,7) and B(6,5) . If the common chords of the circle x^(2)+y^(2)-4x-6y-3=0 and the members of the family of circles pass through a fixed point (a,b), then