Question

which of the following points lies on the circle with equation $(x - 1)^2+(y + 2)^2 = 25?
a. (5,2)
b. (1,-3)
c. (1,7)
d. (6,-2)

Explanation:

Step1: Substitute point (5,2)

Substitute \(x = 5\) and \(y=2\) into \((x - 1)^2+(y + 2)^2\):
\((5 - 1)^2+(2 + 2)^2=4^2+4^2=16 + 16=32
eq25\)

Step2: Substitute point (1,-3)

Substitute \(x = 1\) and \(y=-3\) into \((x - 1)^2+(y + 2)^2\):
\((1 - 1)^2+(-3 + 2)^2=0^2+(-1)^2=0 + 1=1
eq25\)

Step3: Substitute point (1,7)

Substitute \(x = 1\) and \(y = 7\) into \((x - 1)^2+(y + 2)^2\):
\((1 - 1)^2+(7 + 2)^2=0^2+9^2=0+81 = 81
eq25\)

Step4: Substitute point (6,-2)

Substitute \(x = 6\) and \(y=-2\) into \((x - 1)^2+(y + 2)^2\):
\((6 - 1)^2+(-2 + 2)^2=5^2+0^2=25+0 = 25\)

Answer:

D. \((6,-2)\)