Complete the squareto find the center of the circle.

Findthe slopeof the line through the center and the point of tangency. Note that the tangent will be perpendicular to radius line of the circle at the point of tangency, so the perpendicular slope is the slope of the tangent.

Then plug the perpendicular slope and the point of tangency into one of the formulas forequations of straight linesto find the tangent line's equation. (I get the same equation that you did.)

You have the tangent-line's slope, so you know the slope of the two chords. From the circle equation, you know that the radius is 5*sqrt[2].

There's probably a "nicer" way to do this, but one method might be as follows:

The line from the center to the midpoint of one of the chords will have a slope of m = 1. Find the equation, through the center, of the line with this slope.

Draw the circle with its two chords. (The particular scale isn't important. The drawing is just a helpful way of keeping track of stuff.) Draw the line from the center to the midpoint of one of the chords. Also draw the radius lines from the center to either end of this chord. You should now have two identical right triangles.

Label the side of a triangle along the chord as 3sqrt[2] and the side corresponding to a radius line as 5sqrt[2]. Use the Pythagorean Theorem to find the length of the remaining side. This gives the distance of the chord from the center of the circle.

Usethe Distance Formulato find the points on this line that are this distance from the center of the circle.

Then find the equations of the lines containing the chords, using the points you just found with the slope you already know.

If you get stuck, please reply showing how far you have gotten. Thank you!