Answer:
Option B. [tex]R(2,4)[/tex]
Step-by-step explanation:
we know that
If a ordered pair lie on the circle. then the ordered pair must satisfy the equation of the circle
step 1
Find the equation of the circle
we know that
The equation of the circle in center radius form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
r is the radius of the circle
(h,k) is the center of the circle
substitute the values
[tex](x-6)^{2}+(y-1)^{2}=5^{2}[/tex]
[tex](x-6)^{2}+(y-1)^{2}=25[/tex]
step 2
Verify each case
case A) [tex]Q(1, 11)[/tex]
substitute the value of [tex]x=1, y=11[/tex] in the equation of the circle and then compare the results
[tex](1-6)^{2}+(11-1)^{2}=25[/tex]
[tex]25+100=25[/tex] ------> is not true
therefore
the ordered pair Q not lie on the circle
case B) [tex]R(2,4)[/tex]
substitute the value of [tex]x=2, y=4[/tex] in the equation of the circle and then compare the results
[tex](2-6)^{2}+(4-1)^{2}=25[/tex]
[tex]16+9=25[/tex] ------> is true
therefore
the ordered pair R lie on the circle
case C) [tex]S(4,-4)[/tex]
substitute the value of [tex]x=4, y=-4[/tex] in the equation of the circle and then compare the results
[tex](4-6)^{2}+(-4-1)^{2}=25[/tex]
[tex]4+25=25[/tex] ------> is not true
therefore
the ordered pair S not lie on the circle
case D) [tex]T(9,-2)[/tex]
substitute the value of [tex]x=4, y=-4[/tex] in the equation of the circle and then compare the results
[tex](9-6)^{2}+(-2-1)^{2}=25[/tex]
[tex]9+9=25[/tex] ------> is not true
therefore
the ordered pair T not lie on the circle
