Hello, StaryNight!

Given you have the equation of a circle and a point inside it, how do you

calculate the equation of a chord that has that point as its midpoint?

To give an example: let circle be: .

Let the desired midpoint beCode:| | | * * * * | * * ----*---+---*-------*------ * | * * * | o A(2,-1) * | C * * * * | o * * * | (1,-2) * | * | * * | * * | * | * * * |

We find that the equation of the circle is: .

. . It has center and radius 4.

The radius that bisects a chord isperpendicularto the chord.

The slope of is: .

. . Hence, the slope of the chord is: .

Now write the equation of the line through with slope