Statement - 1 : If for any complex number `z, |z-2|+|z-3|=4`, then are bounded by the locus of z is `3pi` sq. units.
Statement -2 : If `|z-a| + |z-b|= |b-a|`, then locus of z will be line segment joining a and b.

Options

A. Statement -1 is True, Statement -2 is a correct explanation for Statement -1
B. Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -1
C. Statement -1 is True, Statement -2 is False.
D. Statement -1 is False, Statement -2 is True.

Answer

To solve the problem, we will analyze both statements step by step.

### Statement 1:
**Given:** For any complex number \( z \), \( |z-2| + |z-3| = 4 \).

1. **Understanding the Expression:**
- The expression \( |z-2| + |z-3| = 4 \) represents the sum of distances from the point \( z \) to the points \( 2 \) and \( 3 \) on the complex plane.
- This is a characteristic of an ellipse, where the sum of the distances from any point on the ellipse to the two foci (in this case, the points \( 2 \) and \( 3 \)) is constant.

2. **Identifying the Foci:**
- The foci of the ellipse are the points \( 2 \) and \( 3 \).
- The distance between the foci is \( |3 - 2| = 1 \).

3. **Finding the Major Axis Length:**
- The constant sum of the distances is \( 4 \). This means the length of the major axis \( 2a = 4 \) which gives \( a = 2 \).

4. **Finding the Distance Between the Foci:**
- The distance between the two foci is \( 1 \), so \( 2c = 1 \) which gives \( c = \frac{1}{2} \).

5. **Using the Relationship Between a, b, and c:**
- We know that \( c^2 = a^2 - b^2 \).
- Plugging in the values:
\[ \left(\frac{1}{2}\right)^2 = 2^2 - b^2 \implies \frac{1}{4} = 4 - b^2 \implies b^2 = 4 - \frac{1}{4} = \frac{16}{4} - \frac{1}{4} = \frac{15}{4} \]
- Thus, \( b = \frac{\sqrt{15}}{2} \).

6. **Calculating the Area of the Ellipse:**
- The area \( A \) of an ellipse is given by the formula \( A = \pi a b \).
- Substituting the values of \( a \) and \( b \):
\[ A = \pi \cdot 2 \cdot \frac{\sqrt{15}}{2} = \pi \sqrt{15} \]

7. **Conclusion for Statement 1:**
- The area \( \pi \sqrt{15} \) is not equal to \( 3\pi \) square units. Therefore, Statement 1 is **false**.

### Statement 2:
**Given:** If \( |z-a| + |z-b| = |b-a| \), then the locus of \( z \) will be the line segment joining \( a \) and \( b \).

1. **Understanding the Expression:**
- The expression \( |z-a| + |z-b| = |b-a| \) indicates that the sum of the distances from point \( z \) to points \( a \) and \( b \) is equal to the distance between \( a \) and \( b \).

2. **Geometric Interpretation:**
- For any point \( z \) to satisfy this equation, it must lie on the line segment joining \( a \) and \( b \). This is because if \( z \) were outside this segment, the sum of the distances would exceed \( |b-a| \) due to the triangle inequality.

3. **Conclusion for Statement 2:**
- Therefore, Statement 2 is **true**.

### Final Conclusion:
- Statement 1 is false, and Statement 2 is true.