find the curve if intersection of the surface x=xy+5 and x+y+z=1 which is neareast to the origin

Question

find the curve if intersection of the surface x=xy+5 and x+y+z=1 which is nearest to the origin

Answer 1

Substitute the expression for x from the first equation into the second equation:

(xy+5) + y + z =1

simplify and rearrange the equation to express y in terms of x and z:

xy+ y +z = 1-5

xy+ y +z = =-4

y(x+ 1) +z = -4

Now, if we want to find the curve nearest to the origin, we can consider the point (0,0,0) as it is the origin. Substitute x=0 into the equation:

y(0+ 1) +z = -4

y +z = -4

So, the curve of intersection closest to the origin is given by the equation y +z = -4

Hope so it will help you