Sketch the trace of the intersection of plane with the sphere:
A)
B)
C)
D)
E)

Question

Sketch the trace of the intersection of plane  with the sphere: ​  ​
A) ​ ​ 
B) ​ ​ 
C) ​ 
D) ​ ​ 
E) ​

Quizplus · Accepted Answer

The plane and sphere intersect in a circle. To find the equation of the circle, we need to substitute the equation of the plane into the equation of the sphere to obtain the intersection curve in terms of x, y and z. We get:
 
x^2 + y^2 + z^2 + 2x + 4y − z − 5 = 0    …(1)
4x − 3y + 2z + 7 = 0     …(2)
We can solve this system of equations to get the equation of the circle in the form of (x−a)^2+(y−b)^2=r^2. However, it is easier to recognize that the center of the circle is (-1, -2, 1) and the radius squared is 7. Hence,
 
(x+1)^2 + (y+2)^2 + (z-1)^2 = 7
 
This matches the equation in choice B. Therefore, B is the correct answer.

Sketch the Trace of the Intersection of Plane with the Sphere