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The text in the image you uploaded reads as follows:

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**1. Ilustrasikan garis yang melewati titik A(4,2) dan B(6,5).**

a. Tentukan persamaan garis.

b. Jika AB merupakan diameter suatu lingkaran, tentukan persamaan lingkaran tersebut.

c. Jika titik C merupakan titik yang berada pada sebarang / yang sembarang pada lingkaran tentukan koordinat titik perpotongan garis AC dengan lingkaran tersebut.

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This problem is written in Indonesian and involves geometric concepts related to lines and circles. Here is a breakdown and solution for each part:

**1. Illustrate the line passing through points \( A(4,2) \) and \( B(6,5) \).**

**a. Determine the equation of the line.**

The formula to find the equation of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)
\]

Substitute \( A(4, 2) \) and \( B(6, 5) \):

\[
y - 2 = \frac{5 - 2}{6 - 4}(x - 4)
\]

Simplify:

\[
y - 2 = \frac{3}{2}(x - 4)
\]

Distribute and simplify further:

\[
y - 2 = \frac{3}{2}x - 6
\]

\[
y = \frac{3}{2}x - 4
\]

So, the equation of the line is:

\[
y = \frac{3}{2}x - 4
\]

**b. If \( AB \) is the diameter of a circle, determine the equation of the circle.**

The center of the circle is the midpoint of \( AB \), and the radius is half the length of \( AB \).

- Midpoint \( M \) is:

\[
M = \left( \frac{4+6}{2}, \frac{2+5}{2} \right) = (5, 3.5)
\]

- The length of \( AB \) (diameter) is:

\[
\text{Length of } AB = \sqrt{(6-4)^2 + (5-2)^2} = \sqrt{4 + 9} = \sqrt{13}
\]

- The radius \( r \) is:

\[
r = \frac{\sqrt{13}}{2}
\]

Thus, the equation of the circle is:

\[
(x - 5)^2 + \left(y - 3.5\right)^2 = \left(\frac{\sqrt{13}}{2}\right)^2
\]

\[
(x - 5)^2 + \left(y - 3.5\right)^2 = \frac{13}{4}
\]

**c. If point \( C \) is any point on the circle, determine the coordinates of the intersection between line \( AC \) and the circle.**

To solve this, we need to:

1. Find the equation of line \( AC \).
2. Solve the system of equations formed by the line equation and the circle equation.

However, without a specific point \( C \), we would typically describe the general approach rather than solve for exact coordinates. The process would involve:

1. Deriving the equation for line \( AC \) using the same method as in part (a).
2. Plugging the line equation into the circle's equation.
3. Solving the resulting quadratic equation to find the intersection points.

Would you like to explore the full intersection details, or do you have any specific questions about this problem?

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### Follow-up Questions:
1. What is the general form of a line equation, and how does it relate to slope-intercept form?
2. How can you determine whether a point lies on a given line?
3. What is the geometric significance of a diameter in relation to a circle?
4. How do you find the length of a line segment using the distance formula?
5. What are the different methods to find the intersection between a line and a circle?

### Tip:
When dealing with geometric problems, always start by visualizing the points and shapes involved to get a clearer understanding of the relationships between them.

Ilustrasikan garis yang melewati titik A(4,2) dan B(6,5). a. Tentukan persamaan garis. b. Jika AB merupakan diameter suatu lingkaran, tentukan persamaan lingkaran tersebut. c. Jika titik C merupakan titik yang berada pada sebarang / yang sembarang pada lingkaran tentukan koordinat titik perpotongan garis AC dengan lingkaran tersebut.

Explore how to find the equation of a line passing through points A(4,2) and B(6,5), and how to determine the equation of a circle with AB as its diameter. Suitable for students in Grades 10-12, this problem covers key concepts in geometry and analytic geometry.

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