Plot `y=|x|,y=|x-2|,` and `y=|x+2|`

x+y=8,x-y=2

Plot the region satisfying |x|+ |y| le 2 and |x|+|y| gt 2 .

Plot y=sinxa n dy=sin(x/2)

3x+y=10,x-y=2

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If l and m vary subject to the condition l^2+m^2=1, then the locus of its circumcenter is (a) (x^2-y^2)^2=x^2+y^2 (b) (x^2+y^2)^2=(x^2-y^2) (c) (x^2+y^2)^2=4x^2y^2 (d) (x^2-y^2)^2=(x^2+y^2)^2

x+y=0,2x-y=9

Let (x,y) = 2x y ^(2) + 3x ^(2) y calculate u _(x) (2,1) and u_(y) (1,-2).

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

If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (X_1, y_1), (x_2, y_2) and (x_3, y_3) are concurrent, prove that |(x_1,y_1,x_1y_1),(x_2,y_2,x_2y_2),(x_3,y_3,x_3y_3)|=0 .