Classify the surface.
$$25 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$
Select the correct answer.
A) A hyperboloid of one sheet with center $( - 3,0,1 )$ and axis parallel to the $z$-axis.
B) A circular paraboloid with vertex $( 0,3,1 )$ and axis the $z$-axis.
C) A cone with axis parallel to the $z$-axis and vertex $( 0,1,1 )$.

Question

Quizplus · Accepted Answer

The equation can be rewritten as $25x^2 + (y-1)^2 - (z-1)^2 = 0$, which represents a cone with its axis parallel to the z-axis and vertex at $(0,1,1)$.

Classify the Surface 25x2+y2−z2−2y+2z=025 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 025x2+y2−z2−2y+2z=0

Classify the Surface $25 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$