Question

select the correct answer.
5
which point lies on the circle represented by the equation $(x + 5)^{2}+(y - 9)^{2}=8^{2}$?
a. $(0,8)$
b. $(13,-9)$
c. $(-5,1)$
d. $(3,17)$
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Explanation:

Step1: Recall the equation of a circle

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. For the given equation \((x + 5)^2+(y - 9)^2=8^2\), the center is \((- 5,9)\) and radius \(r = 8\).

Step2: Check each point

• For point A \((0,8)\):

Substitute \(x = 0\) and \(y = 8\) into the equation \((0 + 5)^2+(8 - 9)^2=25 + 1=26
eq64\).

• For point B \((13,-9)\):

Substitute \(x = 13\) and \(y=-9\) into the equation \((13 + 5)^2+(-9 - 9)^2=324+324 = 648
eq64\).

• For point C \((-5,1)\):

Substitute \(x=-5\) and \(y = 1\) into the equation \((-5 + 5)^2+(1 - 9)^2=0+64=64\).

• For point D \((3,17)\):

Substitute \(x = 3\) and \(y = 17\) into the equation \((3 + 5)^2+(17 - 9)^2=64 + 64=128
eq64\).

Answer:

C. \((-5,1)\)