If (1,2), (4, 3) are the limiting points of a coaxal system , then the equation of the circle in its conjugate system having minimum area is

If the lines 2x+3y+1=0, 3x+2y-1=0 intersect the coordinate axes in four concyclic points then the equation of the circle passing through these four points is

If the circles x²+y²=3a² , x²+y²-6x-8y+9=0 touch externally then a=

The equation to the circles whose radius is 3 and which touches internally the circle x²+y²-4x+6y-12=0 at he point (-1, 1) is

The equation of the chord of contact of the point (4, 2) with respect to the circle x²+y²-5x+4y-3=0 is

The two circles x²+y²=a², x²+y²=c²(c>0) touch each other if

The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x²+y²-4x-2y-11=0 with a pair of radii joining the points of contact of these tangents is

The equation of the normal to the curve (x/a)^2/3+(y/b)^2/3=1 at (a cos³θ, b sin³θ ) is

The distance between the limiting points of the coaxial system x² + y² – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

The condition that the pair of tangents drawn from the origin to the circle x²+y²+2gx+2fy+c=0 may be at right angles is