Solve `x^(2)p^(2)+xpy-6y^(2)=0.`

Solve (x^(2)+y^(2))dx-2xydy=0.

If P_(1), P_(2) and P_(3) are the perimeters of the three circleS and x^(2)+y^(2)+8 x-6 y =0 4 x^(2)+4 y^(2)-4 x-12 y-186 =0 x^(2)+y^(2)-6 x+6 y-9 =0 respectively, then

Solve (x^(2)-ay)dx+(y^(2)-ax)dy=0.

If P is a point such that the ratio of the squares of the ltngths of the tangtnts from P to the circleS x^(2)+y^(2)+2 x-4 y-20=0 and x^(2)+y^(2)-4 x+2 y-44=0 is 2: 3, then the locus of P is a circle with centre

Given that the circleS x^(2)+y^(2)-2 x+6 y+6=0 and x^(2)+y^(2)-5 x+6 y+15=0 touch, the equation of their common tangtnt is

If the circle x^(2)+y^(2)+6 x-2 y+k=0 bisects the circumference of the circle x^(2)+y^(2)+2 x-6 y-15-0 then k=

The equation of the circle which passes through the points of intersection of the circleS x^(2)+y^(2)-6 x=0 and x^(2)+y^(2)-6 y=0 and has centre at ((3)/(2), \(3)/(2)) is

Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-6y=6andx^(2)+y^(2)-4x-12y=9 are in AP.

The two circles x^(2) + y^(2) -2x + 6y + 6 = 0 and x^(2) + y^(2) -5x + 6y + 15 = 0

Find the number of common tangents to the circles x^(2)+y^(2)-8x+2y+8=0andx^(2)+y^(2)-2x-6y-15=0 .