Respuesta :
Answer:
(2, -5) and (6, -1)
Step-by-step explanation:
The equation that represent the coordinate of a circle is
(x-a)^2 + (y-b)^2 = r^2
Where
(a, b) is the coordinate of the center of the circle
r is the radius of the circle
The equation for the circle in this question will be:
(x-2)^2 + (y--1)^2 = 4^2
(x-2)^2 + (y+1)^2 =16
You can put each option into the equation and find it it's true. The points that will fulfill the condition is (2, -5) and (6, -1). The calculation for each point will be:
(x-2)^2 + (y+1)^2 =16
(2-2)^2 + (-5+1)^2 =16
(0)^2 + (-4)^2 =16
16=16
true
(x-2)^2 + (y+1)^2 =16
(6-2)^2 + (-1+1)^2 =16
(4)^2 + (0)^2 =16
16=16
true
The correct option is option (d).
Equation of the circle:
The formula for the equation of the circle with the radius [tex]r[/tex] at the center [tex](h,k)[/tex] is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given the radius of the circle is 4 units with the center [tex](2,-1)[/tex]
Now, substituting the given values into the above formula we get,
[tex](x-2)^2+(y+1)^2=16....(1)[/tex]
Now, satisfying the given points into the equation (1) we get,
[tex](2,-5)=(2-2)^2+(-5+1)^2=16\\(6,-1)=16+0=16[/tex]
So, the points are satisfying to the equation (1) [tex](2, -5)\ and\ (6, -1)[/tex].
Learn more about the equation of the circle:
https://brainly.com/question/519358
