MHB How Do You Find the Equation of a Line Through a Point and a Circle's Center?

[mathdad]

Find an equation of the line that passes through (3, -5) and through the center of the circle given.

x^2 + y^2 + 4x - 4y + 4 = 0

1. Does this question involve completing the square?

2. Must I then write the equation of the circle as

(x - h)2 + (y - k)^2 = r^2 which will disclose the center of the circle not centered at the origin. Yes?

 

[MarkFL]

1 & 2.) Yes, complete the square on both $x$ and $y$ so that you can write the equation of the circle in the form you posted, revealing the center. Then you will have two points on the line, from which you may compute the slope, and then use the point-slope formula to get the equation of the line. (Yes)

 

[mathdad]

1 & 2.) Yes, complete the square on both $x$ and $y$ so that you can write the equation of the circle in the form you posted, revealing the center. Then you will have two points on the line, from which you may compute the slope, and then use the point-slope formula to get the equation of the line. (Yes)

Sometimes, a little thinking goes a long way.