Question

Consider the equation below. X2 + y2 − 2x − 4y − z + 5 = 0 reduce the equation to one of the standard forms. Classify the surface. Ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets sketch the surface. Webassign plot webassign plot webassign plot webassign plot

Answer 1

we are given

$x^2+y^2-2x-4y-z+5=0$

standard form:

We will complete x , y and z square

make all x , y and z terms together  

$x^2-2x+y^2-4y-z+5=0$

$x^2-2x+y^2-4y-z=-5$

$x^2-2*1*x+y^2-2*2*y-z=-5$

$x^2-2*1*x+1^2+y^2-2*2*y+2^2-z=-5+1^2+2^2$

$(x-1)^2+(y-2)^2-z=0$

$z=(x-1)^2+(y-2)^2$

surface:

It is an infinite paraboloid

graph: