Write the equation of a circle and check if the given points satisfy this equation.
D
Practice makes perfect
We are given that the center of ⊙F is at (-4, ) and has a radius of 4. Let's use these information to write the standard equation of the circle F.
(x-(-4))^2+(y- )^2= 4^2 ⇓
(x+4)^2+y^2=16
To determine which of the given points lies on this circle, we can substitute them into the above equation and see if we end with true statements. Let's start with point (4,0).
Since we end with a false statement point (4,0) does not lie on ⊙F. We can check the rest of the points in the same way.
Point
Substitute
Simplify
( 4, 0)
( 4+4)^2+ 0^2? =16
64≠16 *
( 0, 4)
( 0+4)^2+ 4^2? =16
32≠16 *
( 4, 3)
( 4+4)^2+ 3^2? =16
73≠16 *
( -4, 4)
( -4+4)^2+ 4^2? =16
16=16 âś“
( 0, 8)
( 0+4)^2+ 8^2? =16
80≠16 *
As we can see, only point (-4,4) lies on ⊙F. This corresponds with answer D. Let's confirm our answer by plotting the circle and the points in the coordinate plane.
