If `x>0,y>0,x+y=15` and `x^(3)y^(2)` is maximum then `x=..., y=...`

If x+y=4 and x>=0,y>=0 find the maximum value of x^(3)y.

If 2x+3y=0 and 4x-3y=0 then (x+y) equals

The circles whose equations are x^(2)+y^(2)+10x-2y+22=0 and x^(2)+y^(2)+2x-8y+8=0 touch each other. The circle which touch both circles at, the point of contact and passing through (0,0) is, 1) 9(x^(2)+y^(2))-15x-20y=0, 2) 5(x^(2)+y^(2))-18x-80y=0 3) 7(x^(2)+y^(2))-18x-80y=0, 4) x^(2)+y^(2)-9x-40y=0 ]]

A triangle is formed by vertices (0, 0), (x, y), (-x, y) on xy-plane. If the point (x, y) and (-x, y) lies on y =-x^2 54 , then maximum area of triangle is

Find the greatest value of x^(3)y^(4) if 2x+3y=7 and x>=0,y>=0 .

If x^(2)+x=1-y^(2) , where x gt 0, y gt 0 , then find the maximum value of x sqrt(y) .

If OA and OB are equal perpendicular chords of the circles x^(2)+y^(2)-2x+4y=0, then the equations of OA and OB are,where O is the origin.3x+y=0 and 3x-y=03x+y=0 and 3y-x=0x+3y=0 and y-3x=0x+y=0 and x-y=0 and y-3x=0