10x+4y+11xy
10x - 3y + 2x - 4y =(10x + 2x) + (-3y - 4y) =12x - 7y
If: 4y+10x = 16Then: 4y = -10x+16And: y = -2.5x+4
10x + 2y + 8z - 5x + 4z - 4y = 10x - 5x + 2y - 4y + 8z + 4z = (10 - 5)x + (2 - 4)y + (8 + 4)z = 5x - 2y + 12z
Complete the squares: x2 - 10x + 25 + y2 + 4y + 4 - 52 = 25 + 4 = 29 x2 - 10x + 25 + y2 + 4y + 4 = 52 + 29 = 81 So the radius is sqrt(81) = 9
10x+4y+11xy
10x - 3y + 2x - 4y =(10x + 2x) + (-3y - 4y) =12x - 7y
If: 4y+10x = 16Then: 4y = -10x+16And: y = -2.5x+4
10x+2x-3y-4y=12x-7y
10x + 2y + 8z - 5x + 4z - 4y = 10x - 5x + 2y - 4y + 8z + 4z = (10 - 5)x + (2 - 4)y + (8 + 4)z = 5x - 2y + 12z
6-2x-8+3+12x+4y 10x+4y+1 Note that - -3 = +3 and that - -4y = +4y
Complete the squares: x2 - 10x + 25 + y2 + 4y + 4 - 52 = 25 + 4 = 29 x2 - 10x + 25 + y2 + 4y + 4 = 52 + 29 = 81 So the radius is sqrt(81) = 9
Given: x2 + y2 - 10x + 4y + 4 = 0 First, we'll move our constants to the right: x2 + y2 - 10x + 4y = -4 Then group terms with the same variables together: x2 - 10x + y2 + 4y = -4 Then complete the squares: x2 - 10x + 25 + y2 + 4y + 4 = -4 + 25 + 4 (x - 5)2 + (y + 2)2 = 25 And there we have it. This is an equation for a circle whose center point is at (5, -2), with a radius of √25, which equals 5.
3x - 2y + 7x + 4y = 3x + 7x - 2y +4y = (3+7)x + (-2+4)y = 10x + 2y
6x - 4y
x= zβ4y/10 β y= zβ10x/4
x2 + y2 - 10x + 4y - 52 = 0 x2 - 10x + y2 + 4y = 52 Complete the square (x2 - 10x + 25) + (y2 + 4y + 4) = 52 + 25 + 4 (x - 5)2 + (y + 2)2 = 81 (x - 5)2 + (y - -2)2 = 92 This is the equation of a circle with center (5, -2), and radius 9.