Question

A circle has a center located at (-2, 4) and a radius of length 10. Does the point (4, - 4) lie on this circle? Explain how you arrived at your answer.​

Answer 1

Answer: Yes, (4, - 4) lies on this circle.

Step-by-step explanation:

Equation of circle:$(x-h)^2+(y-k)^2=r^2$ , where (h,k) = center , r = radius

Given: A circle has a center located at (-2, 4) and a radius of length 10.

i.e. (h,k) =(-2,4) and r= 10

Equation of circle will be:

$(x-(-2))^2+(y-4)^2=10^2\\\\\Rightarrow\ (x+2)^2+(y-4)^2=100$ (i)

If (4, - 4) lies on this circle , then it must satisfy the above equation.

To check put x= 4 , y=-4 in (i)

$(4+2)^2+(-4-4)^2=100\\\\\Rightarrow\ 6^2+(-8)^2=100\\\\\Rightarrow\ 36+64=100\\\\\Rightarrow\ 100=100$ which is true.

Hence, (4, - 4) lies on this circle.