Circle

To find the length of the X-axis intercept for the circle given by the equation:

we follow these steps:

1. Compare with Standard Form:
The standard form of a circle's equation is:


Comparing coefficients, we find:

2. X-Intercept Formula:
The length of the X-axis intercept is given by:

3. Substitute Values:
Plugging in the values for and :

4. Simplify the Expression:
Convert 2 to fourths and subtract:


Now take the square root:

Final Answer:
The length of the X-axis intercept is .

We are given the equations:

1. (i)
2. (ii)

Subtracting (ii) from (i):

Substituting into equation (i):

Therefore, the points of intersection are and . So the values for and are correct.

Final Answer: The final answer is

To determine the position of the point relative to the circles and , we evaluate the circle equations at this point.

1. Evaluation for Circle :
Given the circle equation :


Simplify step-by-step:

Conclusion: Since , the point lies outside circle .

2. Evaluation for Circle :
Given the circle equation :


Simplify step-by-step:

Conclusion: Since , the point lies inside circle .

3. Final Determination:
The point lies:
- Outside of circle (since )
- Inside of circle (since )

Final Answer:
The point lies .