Question

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. $(3,17)$

Explanation:

Step1: Substitute \(x = 0,y = 8\) into the equation

$$(0 + 5)^2+(8 - 9)^2=25 + 1=26 eq64$$

Step2: Substitute \(x = 13,y=-9\) into the equation

$$(13 + 5)^2+(-9 - 9)^2=324+324 = 648 eq64$$

Step3: Substitute \(x=-5,y = 1\) into the equation

$$(-5 + 5)^2+(1 - 9)^2=0+64=64$$

Step4: Substitute \(x = 3,y = 17\) into the equation

$$(3 + 5)^2+(17 - 9)^2=64 + 64=128 eq64$$

Answer:

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