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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryPlaneMedium2 minQB

MathematicsMediumsingle choice

If the plane $2 x + 3 y + 6 z + k = 0$ is tangent to the sphere $x^{2} + y^{2} + z^{2} + 2 x - 2 y + 2 z - 6 = 0$ , then a value of $k$ is

Options:

Answer:

Solution:

The centre is (-1, 1, -1) and the radius is 3. The distance of the centre from the plane is $\frac{- 2 + 3 - 6 + k}{4 + 9 + 36} = \frac{∣ k - 5∣}{7} = 3$ , so $∣ k - 5∣ = 21$ and $k = 26$ or $k = - 16$ . Of the options, only 26 appears.

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Plane

⏱ 2mℹ️ Source: QB

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