Answer:
Determine the equation of the circle.
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Given:
Substitute the given values into the formula to determine the equation of the circle:
[tex]\implies (x-0)^2+(y-0)^2=7^2[/tex]
[tex]\implies x^2+y^2=49[/tex]
Given point: [tex](-3,2\sqrt{10})[/tex]
Input the x and y values of the given point into the derived circle equation. If it equals 49, then the point is on the circle:
[tex]\implies (-3)^2+(2 \sqrt{10})^2=9+40=49[/tex]
Therefore, the given point is on the circle centered at the origin with a diameter of 14 units.
