A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fish pond at a given location and specify your center point and
radius. Write your circular fish pond equation. On your coordinate plane, identify the point to
represent the location of the water main connection. Construct the pipe so that it is tangent
to the fish pond from the water main. Include all steps to creating a tangent line, as
discussed in this lesson. Submit your final graph. You may do this by hand, using a compass
and straightedge, or using a graphing software program.

  see below

Step-by-step explanation:

We choose a fish pond of radius 3 centered at (x, y) = (0, 3). The equation of the circle is ...

  (x -0)^2 +(y -3)^2 = 3^2

  x^2 +(y -3)^2 = 9

At this location it is easy to draw a radius along the y-axis to a point of tangency at the origin. That radius is a vertical line, so the tangent line will be perpendicular--a horizontal line.

A horizontal line through the origin has equation y = 0, and its point of intersection with this circle is (0, 0).

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Comment on the question

You haven't elaborated on what the lesson discussed, so we have no idea what steps you want included.