Q77 / 150 · MHT CET 2023 (09 May Shift 1) · Mathematics

The foot of the perpendicular drawn from the origin to the plane is $(4,-2,5)$, then the Cartesian equation of the plane is

  • Correct answer
    A
    4x-2y+5z=45
  • B
    -4x+2y+5z=45
  • C
    4x-2y+5z+45=0
  • D
    4x+2y-5z+45=0

Solution

Substitute $x=4, y=-2, \mathrm{z}=5$ in all options. $\therefore \quad$ For option A $\begin{aligned} 4 x-2 y+5 z & =4(4)-2(-2)+5(5) \\ & =16+4+25 \\ & =45 \end{aligned}$ $\therefore \quad$ Only option A is satisfied by $(4,-2,5)$

Hence, the correct answer is option: 'A'.

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