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 is perpendicular to the chord.
The slope of is: .
. . Hence, the slope of the chord is: .
Now write the equation of the line through with slope