Question

1 multiple choice 1 point which of these points lies on the circle with center (2, 3) and radius 2? (-1,0) (1,3) (3,4) (4,3)

Explanation:

Step1: Recall circle - equation formula

The equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2+(y - k)^2=r^2$. Here, $h = 2$, $k = 3$, and $r = 2$, so the equation is $(x - 2)^2+(y - 3)^2=4$.

Step2: Test point $(-1,0)$

Substitute $x=-1$ and $y = 0$ into the equation: $(-1 - 2)^2+(0 - 3)^2=(-3)^2+( - 3)^2=9 + 9=18
eq4$.

Step3: Test point $(1,3)$

Substitute $x = 1$ and $y = 3$ into the equation: $(1 - 2)^2+(3 - 3)^2=(-1)^2+0^2=1
eq4$.

Step4: Test point $(3,4)$

Substitute $x = 3$ and $y = 4$ into the equation: $(3 - 2)^2+(4 - 3)^2=1^2+1^2=2
eq4$.

Step5: Test point $(4,3)$

Substitute $x = 4$ and $y = 3$ into the equation: $(4 - 2)^2+(3 - 3)^2=2^2+0^2=4$.

Answer:

D. $(4,3)$