Question

Does the point (2√3, 2) lie on the circle that is centered at the origin and contains the point (0, -4)? Explain?

Answer 1

The answer to your question is Yes, the point P lies on the circle

Explanation:

Data

P (2
`√(3)`, 2)

Center (0, 0)

Q (0, -4)

Process

1.- Find the radius of the circle

dCQ =
`\sqrt{(0-0)^(2)+ (-4 + 0)^(2)}`

dCQ =
`\sqrt{0^(2) + (-4)^(2)}`

dCQ =
`√(16)`

dCQ = 4

2.- Find the equation of the circle

(x - 0)² + (y - 0)² = 4²

-Simplification

x² + y² = 16

3.- Substitute P in the equation of the circle

(2
`√(3)`)² + (2)² = 16

4(3) + 4 = 16

12 + 4 = 16

16 = 16

4.- Conclusion

The point (2
`√(3)`, 2) lies on the circle because when we evaluate the equation of the circle with this point, we get the length of the radius.