find the equation of a line equidistant from the lines `y=10\ a n d\ y=-2.`

Explanation

The lines `y=10` and `y=-2` pass through the points `(0,10)` and `(0,-2),` respectively. Let `(h, k)` be the mid-point of the line joining the points `(0,10)` and` (0,-2).`


Therefore`(h, k)=(0, frac(10-2)2)=(0,4)`


The given lines are parallel to the x-axis and the required line is equidistant from these lines.
Hence, the required line is parallel to the x-axis, which is given by y=k.

This line passes through `(0,4).`


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