**Sol 1 ** Using the slope-intercept form, where when ,
so and therefore . Therefore the line has equation
.

**Sol 2** The slope of the line is given by
, so
its equation is given by or .

**Sol 3** Since the two points have the same x-coordinate, the line passing
through these points is vertical; so its equation is simply .

**Sol 4** Solving the equation for y gives , so its
slope is given by and therefore a perpendicular line has slope
given by
. Using the point-slope form, we get
the equation
; and simplifying gives .

**Sol 5** The perpendicular bisector will pass through the midpoint of the
line segment, which is given by
. The slope
of the line segment is given by
, so the slope of the
perpendicular bisector will be
. Therefore the
perpendicular bisector has the equation or .

**Sol 6** The line through the two given points has slope
, so the line we want will also have slope since the
two lines are parallel. Thus its equation is given by or
.

**Sol 7** The tangent line at the point will be perpendicular to the
line segment from the center to the point . Since this
line segment has slope
, the tangent line has the
slope
. Since the tangent line passes through the
point , its equation is
or .

**Sol 8** Multiplying the first equation by 2 gives , and then
subtracting the second equation from the first gives
or . Then substituting back into the first equation gives
so . Therefore is the point of intersection of the lines.

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