Intersection of a sphere by a plane is called circular section. (i) If the plane intersects the sphere in more than one different points, then the section is called a circle. (ii) If the circle of sec

Question

Intersection of a sphere by a plane is called circular section. (i) If the plane intersects the sphere in more than one different points, then the section is called a circle. (ii) If the circle of section is of greatest possible radius, then the circle is called great circle. (iii) If the radius of circular section is zero, then the section is a point circle. (iv) If the plane does not meet the sphere at all, then the section is an imaginary circle. Sphere $x^{2} + y^{2} + z^{2} = 4$ is intersected by the plane $2 x + 3 y + 6 z + 7 = 0$ in

Options:

Answer:

B

Solution:

Distance of the centre (0, 0, 0) from the plane is $\frac{7}{4 + 9 + 36} = \frac{7}{7} = 1 < 2$ (radius). So the section is a real circle but not a great circle.

TestHub · Accepted Answer

Distance of the centre (0, 0, 0) from the plane is 4 + 9 + 36 ​ 7 ​ = 7 7 ​ = 1 < 2 (radius). So the section is a real circle but not a great circle.

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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