Question 896289
the formula for a circle that you need is:


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


your equation can be converted into this form easily since it's pretty much set up to allow you to do without a lot of manipulation.


your equation is:


x^2-2x+1+y^2+2y+1=25


this can be separated into 2 parts.


(x^2 - 2x + 1) + (y^2 + 2y + 1) = 25


the first part can be factored into (x-1)^2.
the second part can be factored into (y+1)^2.


your equation becomes:


(x-1)^2 + (y+1)^2 = 25


now it's in  the form of (x-h)^2 + (y-k)^2 = r^2


h is the x-coordinate of the center of the circle.
k is the y-coordinate of the center of the circle.
r is the radius of the circle.


this means that h is equal to 1 because x-h becomes x-1 when h is equal to 1.


this means that k is equal to -1 because y-k becomes y-(-1) = y+1 when k is equal to -1.


the chord is passing through the point (1,-1) which is the center of the circle.


if the chord passes through the center of the circle, then the chord is a diameter of the circle.


the radius of the circle is 5 since r^2 = 25.


the diameter is equal to 2 * the radius, so the diameter must be equal to 10.


that's your answer.


the chord that passes through the point (1,-1) is equal to 10 units in length.