If `x:y=2:3` and `2:x=1:2`,then y=?

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

If X and Y are 2xx2 matrices, then solve the following matrix equations for X and Y 2X+3Y=[[2,3],[4,0]],3X+2Y=[[-2,2],[1,-5]]

Let C_(1):y=x^(2)sin3x,C_(2):y=x^(2)and C_(3):y=-y^(2), then

Find area of region bounded by y = x^2 – 3x + 2, x = 1, x = 2 and y = 0 .

The equation of the line intersection of the planes 4x+4y-5z=12 and 8x+12y-13z=32 can be written as: (A) x/2=(y-1)/3=(z-2)/4 (B) x/2=y/3=(z-2)/4 (C) (x-1)/2=(y-2)/3=z/4 (D) (x-1)/2=(y-2)/(-3)=z/4

If (x_1-x_2)^2+(y_1-y_2)^2=a^2 , (x_2-x_3)^2+(y_2-y_3)^2=b^2 , (x_3-x_1)^2+(y_3-y_1)^2=c^2 , and 2s=a+b+c then what willl be the value of 1/4|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|^2

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then x_1+x_2+x_3+x_4=0 y_1+y_2+y_3+y_4=0 x_1x_2x_3x_4=C^4 y_1y_2y_3y_4=C^4

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then x_1+x_2+x_3+x_4=0 y_1+y_2+y_3+y_4=0 x_1x_2x_3x_4=C^4 y_1y_2y_3y_4=C^4

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .