Answer:
Yes, the distance from [tex](-2,0)\ to\ (1,\sqrt{7})\ is\ 4\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the equation of the circle
we know that
The equation of the circle is equal to
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex](h,k)=(-2,0)[/tex]
and the radius is equal to the distance between the center and the point (-2,4)
so
[tex]r=4\ units[/tex] ----> look at the graph
substitute in the equation
[tex](x+2)^{2}+(y)^{2} =4^{2}\\(x+2)^{2}+(y)^{2} =16[/tex]
step 2
If the distance between the center and the point is equal to the radius of the circle , then the point lie on the circle
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}\\A(-2,0)\\B(1,\sqrt{7})[/tex]
substitute the values
[tex]d=\sqrt{(\sqrt{7}-0)^{2}+(1+2)^{2}}\\d=\sqrt{7+9}\\d=\sqrt16}=4\ units[/tex]
therefore
the point lie on the circle
