`S(x ,y)=0` represents a circle. The equation `S(x ,2)=0` gives two identical solutions: `x=1` . The equation `S(1,y)=0` given two solutions: `y=0,2.` Find the equation of the circle.

S(x,y)=0 represents a circle. The equation S(x,2)=0 gives two identical solutions x=1 and the equation S(1,y)=0 gives two distinct solutions y=0,2 then the equatino of the circle is

Find the solution of the pair of equations: x-y+1=0, 3x+2y-12=0

The solution of the equation (x^(2)y+x^(2))dx+y^(2)(x-1)dy=0 is given by

Find the sum of all the real solution (s) to the equation (x+y)^(2)=(x+1)(y-1).

Find the equation of hyperbola having foci S(2, 1) and S'(10, 1) and a straingt line x+y-9=0 as its tangent. Also, find the equation of its director circle.

The equations of two diameters of a circle are x-2y+1=0 and x+y-2=0 and the length of the chord intercepted on the straight line 3x+4y+8=0 by the circle is 6 units. Find the equation of the circle.

Find a particular solution of the differential equation (x+1)(dy)/(dx)=2e^(-y)-1 given that y=0x=0

Find the equation of the two tangents from the point (0,1) to the circle x^(2)+y^(2)-2x+4y=0

y=mx is a chord of equation of circle x^(2)+y^(2)-2ax=0. Find the equation of circle this chord is diameter of a circle.