If #x-y=2# is the equation of a chord of the circle #x^2+y^2+2y=0#.Find the equation of the circle of which this chord is a diameter.?
the equation of the chord
#" "color (magenta)(x-y=2.....)#
the equation of the circle
From these two equations we get
Inserting in  we get
So the coordinates of points intersections of the chord with the circles are
The line segment of the chord is also the diameter of a circle.
So equation of this circle having diameter
This is the required equation of the circle
We will solve this Problem using the following Result R :
R : The Equation (eqn.) of a Circle that passes through
the Points (pt.) of Intersection of a Circle S & Line L
Note that, the Reqd. Circle, say
Applying R, we may suppose that,
This shows that the Centre
Now, given that
already derived by Respected dk_ch Sir!