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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