MHB Finding the Equation of a Circle Given Specific Conditions

[mathdad]

Determine the equation of the circle that satisfies the given conditions. Write the equation in standard form.

The circle passes through (-4, 1) and its center is the midpoint of the line segment joining the centers of the two circles x^2 + y^2 - 6x - 4y + 12 = 0 and x^2 + y^2 - 14x + 47 = 0.

I would like the steps for me to solve this interesting problem.

 

[MarkFL]

I would begin by determining the centers of the two given circles, so that we can determine the mid-point of the line segment joining those centers. So, rewrite the two given circles in the form:

$$(x-h)^2+(y-k)^2=r^2$$

What do you get?

 

[mathdad]

I would begin by determining the centers of the two given circles, so that we can determine the mid-point of the line segment joining those centers. So, rewrite the two given circles in the form:

$$(x-h)^2+(y-k)^2=r^2$$

What do you get?

Must I complete the square for both circles?

 

[MarkFL]

Must I complete the square for both circles?

Yes, for both circles you want to complete the square for both x and y to get them in the desired form from which you can read off the coordinates of the centers. :D

 

[mathdad]

Yes, for both circles you want to complete the square for both x and y to get them in the desired form from which you can read off the coordinates of the centers. :D

Good. I will try later.