Describe the given set of points with a single equation or with a pair of equations.
-The circle in which the plane through the point (5, -8, -2) perpendicular to the x-axis meets the sphere of radius 13 centered at the origin.
A) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 169$ and $z = 5$
B) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 144$ and $y = 5$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 119$ and $y = 5$
D) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 169$ and $x = 5$

Question

Describe the given set of points with a single equation or with a pair of equations.
-The circle in which the plane through the point (5, -8, -2) perpendicular to the x-axis meets the sphere of radius 13 centered at the origin. 
A) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 169$ and $z = 5$
B) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 144$ and $y = 5$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 119$ and $y = 5$
D) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 169$ and $x = 5$

Quizplus · Accepted Answer

The plane passing through the point (5,-8,-2) and perpendicular to the x-axis has equation x=5. Thus, any point on the circle of intersection must satisfy x=5. 
Also, the circle lies on the sphere of radius 13 centered at the origin. Thus, any point on the circle must satisfy the equation x^2+y^2+z^2=169. 
So, the equation for the circle is x=5 and x^2+y^2+z^2=169, which simplifies to x^2+y^2+z^2=169 and y^2+z^2=144 (by substituting x=5 into the second equation). This is the equation of a circle in the yz-plane centered at the origin with radius 12. The correct answer is D, which gives x=5 as the equation for the plane and x^2+y^2+z^2=169 as the equation for the sphere.

Describe the Given Set of Points with a Single Equation x2+y2+z2=169x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 169x2+y2+z2=169

Describe the Given Set of Points with a Single Equation $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 169$