How do you write the general form of a circle given characteristics. Center: (−5, 1); solution point: (0, 0)?

1 Answer
sente
Dec 19, 2015

#(x + 5)^2 + (y-1)^2 = 26#

Explanation:

A circle of radius #r#, centered at #(h, k)# has the form

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

From the given information, we have #h = -5# and #k = 1#. To find #r#, we need only find the distance from the center #(h, k)# to a point on the circle. As #(0, 0)# is such a point, applying the distance formula gives us

#r = sqrt((-5-0)^2 + (1-0)^2) = sqrt(26)#

Thus the desired equation is

#(x-(-5))^2 + (y - 1)^2 = sqrt(26)^2#

or, simplifying,

#(x + 5)^2 + (y-1)^2 = 26#

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