Answer to Question #145221 in Analytic Geometry for Dhruv rawat

Question #145221
The xy-plane intersects the sphere x^2+y^2+z^2+2x+2y-z=2 in a great circle.
True or false with full explanation
1
Expert's answer
2020-11-24T14:24:07-0500

"x^2+y^2+z^2+2x+2y-z=2,"

"(x+1)^2-1+(y+1)^2-1+(z-\\frac12)^2-\\frac14=2,"

"(x+1)^2+(y+1)^2+(z-\\frac12)^2=4\\frac14."

The xy-plane intersects the sphere in a great circle, when coordinates of the centre are "(x_0, y_0, 0)."

We have "(-1, -1, \\frac12)."

The xy-plane does not intersect the sphere in a great circle.


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