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. The sphere $x^{2} + y^{2} + z^{2} + 2 x + 6 y - 8 z - 1 = 0$ is intersected by the plane $x + 2 y - 3 z - 7 = 0$ in

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Answer:

D

Solution:

Distance of the centre (-1, -3, 4) from the plane is $\frac{∣ - 1 - 6 - 12 - 7∣}{1 + 4 + 9} = \frac{26}{14} \approx 6.95$ , and the radius is $1 + 9 + 16 + 1 = 33 \approx 5.2$ . Since the distance exceeds the radius, the section is an imaginary circle.

TestHub · Accepted Answer

Distance of the centre (-1, -3, 4) from the plane is 1 + 4 + 9 ​ ∣ − 1 − 6 − 12 − 7∣ ​ = 14 ​ 26 ​ ≈ 6.95 , and the radius is 1 + 9 + 16 + 1 ​ = 3 3 ​ ≈ 5.2 . Since the distance exceeds the radius, the section is an imaginary circle.

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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