Let C be the locus of a point the sum of whose distances from the points `S(sqrt3,0) and S'(-sqrt3,0) " is " 4.`
Statement-1: The curve C cuts off intercept `2sqrt3` from the line 2y-1=0
Statement-2: The equation of the centre C is `x^(2)+ 8y^(2)=5`

Options

A. Statement-1 is True, Statement-2 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

Explanation

To solve the problem, we need to determine the locus of a point such that the sum of its distances from two fixed points \( S(\sqrt{3}, 0) \) and \( S'(-\sqrt{3}, 0) \) is equal to 4. This describes an ellipse.

### Step-by-Step Solution:

1. **Identify the foci and the sum of distances**:
The foci of the ellipse are \( S(\sqrt{3}, 0) \) and \( S'(-\sqrt{3}, 0) \). The sum of the distances from any point on the ellipse to the foci is given as 4.

2. **Determine the distance between the foci**:
The distance between the two foci \( S \) and \( S' \) is:
\[ d = 2c = 2\sqrt{3} \]
where \( c \) is the distance from the center of the ellipse to each focus.

3. **Relate the lengths of the axes**:
For an ellipse, the relationship between the semi-major axis \( a \), semi-minor axis \( b \), and the distance to the foci \( c \) is given by:
\[ c^2 = a^2 - b^2 \]
Here, the total distance (major axis) is 4, so:
\[ 2a = 4 \implies a = 2 \]

4. **Calculate \( c \)**:
From the distance between the foci:
\[ 2c = 2\sqrt{3} \implies c = \sqrt{3} \]

5. **Find \( b \)**:
Using the relationship \( c^2 = a^2 - b^2 \):
\[ (\sqrt{3})^2 = (2)^2 - b^2 \implies 3 = 4 - b^2 \implies b^2 = 1 \implies b = 1 \]

6. **Write the equation of the ellipse**:
The standard form of the ellipse centered at the origin is:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
Substituting the values of \( a \) and \( b \):
\[ \frac{x^2}{4} + \frac{y^2}{1} = 1 \]

7. **Check the intercepts with the line**:
The line given is \( 2y - 1 = 0 \) or \( y = \frac{1}{2} \). Substituting \( y = \frac{1}{2} \) into the ellipse equation:
\[ \frac{x^2}{4} + \frac{(\frac{1}{2})^2}{1} = 1 \implies \frac{x^2}{4} + \frac{1}{4} = 1 \implies \frac{x^2}{4} = \frac{3}{4} \implies x^2 = 3 \implies x = \pm \sqrt{3} \]
Thus, the points of intersection are \( (\sqrt{3}, \frac{1}{2}) \) and \( (-\sqrt{3}, \frac{1}{2}) \).

8. **Calculate the length of the intercept**:
The length of the intercept \( PQ \) is:
\[ PQ = \sqrt{3} - (-\sqrt{3}) = 2\sqrt{3} \]

### Conclusion:
- **Statement 1** is true: The curve \( C \) cuts off an intercept of \( 2\sqrt{3} \) from the line \( 2y - 1 = 0 \).
- **Statement 2** is false: The correct equation of the ellipse is \( \frac{x^2}{4} + y^2 = 1 \), not \( x^2 + 8y^2 = 5 \).