Answer:
Yes,the distance from (-2,0) to [tex](1,\sqrt 7)[/tex] is 4 units
Step-by-step explanation:
We are given that
Center of circle=(-2,0)
Let point P([tex]1,\sqrt 7)[/tex]
We have to find that ([tex]1,\sqrt 7)[/tex] lies on the circle or not.
Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
Distance between Center (-2,0) and (-2,4)=Radius of circle=R
[tex]R=\sqrt{(-2+2)^2+(4-0)^2}[/tex]
[tex]R=\sqrt{(4)^2}=4[/tex]units
Distance between (-2,0) and (1,[tex]\sqrt 7[/tex])=[tex]\sqrt{(1+2)^2+(\sqrt 7-0)^2}=4[/tex]units
Distance between point P([tex]1,\sqrt 7[/tex]) and center (-2,0)=Radius of circle
Hence, the point P[tex](1,\sqrt 7)[/tex] lies on the circle.
Yes,the distance from (-2,0) to [tex](1,\sqrt 7)[/tex] is 4 units
