Find the equation of the plane with intercept 3 on the $y$-axis and parallel to ZOX plane.

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Find the equation of the plane with intercept 3 on the $y$ -axis and parallel to ZOX plane.

Find the equation of the plane with intercept 3 on the $y$ -axis and parallel to ZOX plane.

Solution:

It is known to us that the equation of the plane $\mathrm{ZOX}$ is $\mathrm{y}=0$
Therefore, the equation of plane parallel to $\mathrm{ZOX}$ is of the form, $\mathrm{y}=\mathrm{a}$
As the y-intercept of the plane is $3, a=3$ and the point $(2,2,1)$ .
As a result, the required equation of the plane is y = 3