Give a geometric description of the set of points whose coordinates satisfy the given conditions.
-$$x ^ { 2 } + y ^ { 2 } \leq 1 , z = 7$$
A) All points within the parabola $x ^ { 2 } + y ^ { 2 } = 1$ in the plane $z = 7$
B) All points on the cylinder with radius 1 along the $z$-axis
C) All points on or outside of the circle $x ^ { 2 } + y ^ { 2 } = 1$ and in the plane $z = 7$
D) All points on or within the circle $x ^ { 2 } + y ^ { 2 } = 1$ and in the plane $z = 7$

Question

Quizplus · Accepted Answer

The equation $x^2+y^2\leq 1$ is the inequality for the interior and boundary of the circle with radius 1 centered at the origin in the $xy$-plane. The equation $z=7$ restricts all points to lie on the plane $z=7$. Therefore, the set of points that satisfy $x^2+y^2\leq 1$ and $z=7$ is the set of points that lie within or on the circle with radius 1 centered at the origin in the plane $z=7$. In other words, the set is the disk with radius 1 and center $(0,0,7)$. Therefore, the correct choice is $	extbf{(D)}$.

Give a Geometric Description of the Set of Points Whose x2+y2≤1,z=7x ^ { 2 } + y ^ { 2 } \leq 1 , z = 7x2+y2≤1,z=7

Give a Geometric Description of the Set of Points Whose $x ^ { 2 } + y ^ { 2 } \leq 1 , z = 7$