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MHT CET202525 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

In 3-dimensional space, the equation x^2-8 x+12=0 represents ....

Options

  1. Atwo straight lines
  2. Ba pair of straight lines passing through the origin
  3. C2 planes parallel to YZ-plane
  4. D2 planes parallel to XZ-plane

Correct answer

C. 2 planes parallel to YZ-plane

Step-by-step solution

The quadratic equation x^2 - 8x + 12 = 0 factors as (x - 2)(x - 6) = 0 , yielding solutions x = 2 and x = 6 . In three-dimensional space, equations of the form x = k represent planes parallel to the YZ-plane. Specifically, x = 2 and x = 6 define two distinct planes, both parallel to the YZ-plane and located at distances of 2 and 6 units from it along the positive X-axis. Among the options, C) 2 planes parallel to YZ-plane correctly describes this configuration, as planes parallel to the XZ-plane would instead be gi

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