Question 896289: what will be the length of the chord of the circle x^2-2x+1+y^2+2y+1=25 , passing through the point (1,-1)? can you please let me know the formula used here as well?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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