If the circles of same radius `a` and centers at `(2, 3) and (5, 6)` cut orthogonally, then find `a.`

If the curves a y+x^2=7 and x^3=y cut orthogonally at (1,1) , then find the value adot

C_1 and C_2 are circle of unit radius with centers at (0, 0) and (1, 0), respectively, C_3 is a circle of unit radius. It passes through the centers of the circles C_1a n dC_2 and has its center above the x-axis. Find the equation of the common tangent to C_1a n dC_3 which does not pass through C_2dot

The radius of the circle touching the line 2x + 3y +1 = 0 at (1,-1) and cutting orthogonally the circle having line segment joining (0, 3) and (-2,-1) as diameter is

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

The centre of the circle S = 0 lies on the line 2x -2y + 9 = 0 and S = 0 cuts orthogonally the circle x^2 + y^2 = 4 . Show that S = 0 passes through two fixed points and also find the co-ordinates of these two points.

Two congruent circles with centered at (2, 3) and (5, 6) which intersect at right angles, have radius equal to (a) 2 sqrt(3) (b) 3 (c) 4 (d) none of these

If the two circles 2x^(2) +2y^(2) -3x+6y+k=0 and x^(2) +y^(2) -4x +10y +16=0 cut orthogonally, then the vlaue of k is-

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 centre is

Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x cut orthogonally.

Find the equation of the circle with radius 5 whose center lies on the x-axis and passes through the point (2, 3).