MHB Finding the Equation of a Line through a Point and Circle Center?

[mathdad]

Find an equation of the line passing through (3, -5) and through the center of the circle 4x^2 + 8x + 4y^2 - 24y + 15 = 0.

Does this problem involve completing the square?

Must I express the above circle in the form (x - h)^2 + (y - k)^2 = r^2?

The center is the point (h, k), right?

I must then find the slope of the points (3, -5) and (h, k), right?

I then use the point-slope formula and proceed as usual.

 

[Evgeny.Makarov]

Yes, you are correct. You may use the following equation of the line passing through (x1, y1) and (x2, y2).

\[
\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}
\]

if y2 - y1 = 0, then the equation is y = y1. If x2 - x1 = 0, then the equation is x = x1.

 

[mathdad]

Cool. Good to know that I understood the question correctly.