y=2at^(2)quad y=at^(4)

If x/y = (a + 2)/(a - 2) , then show that (x^(2) - y^(2))/(x^(2) + y^(2)) = (4a)/(a^(2) + 4) .

Statement 1: The equations of the straight lines joining the origin to the points of intersection of x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-2x-4y-4=0 is x-y=0 . Statement 2: y+x=0 is the common chord of x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-2x-4y-4=0

The degree of the differential equation (y' - 2y '' ) ^(2) = (y')^(4) :

Area bounded by x ^(2) y ^(2)+ y ^(4)-x ^(2)-5y ^(2)+4=0 is equal to :

y^(2)=4x, y^(2)=4(4-x)

The equation of the circle having the center on the line x+2y-3=0 and passing through the point intersection of the circles x^(2)+y^(2)-2x-4y+1=0andx^(2)+y^(2)-4x-2y+4=0 is x^(2)+y^(2)-6x+7=0x^(2)+y^(2)-3u-2y+4=0x^(2)+y^(2)-2x-2y+1=0x^(2)+y^(2)+2x-2y+4=0

If sin^(-1)x + sin^(-1)y = pi/2 prove that 2(x^(2) -x^(2)y^(2) + y^(2)) = 1 + x^(4) +y^(4) .

Find the compound ratio of the ratios (x + y) : (x - y), (x^(2) + y^(2)) : (x + y)^(2) " and " (x^(2)-y^(2))^(2) : (x^(4) - y^(4)) .