Statement-1: The line `x+9y-12=0` is the chord of contact of tangents drawn from a point P to the circle `2x^(2)+2y^(2)-3x+5y-7=0`.
Statement-2: The line segment joining the points of contacts of the tangents drawn from an external point P to a circle is the chord of contact of tangents drawn from P with respect to the given circle

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 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 analyze the two statements given regarding the chord of contact of tangents drawn from an external point to a circle.

### Step-by-Step Solution:

1. **Identify the Circle's Equation**:
The equation of the circle is given as:
\[ 2x^2 + 2y^2 - 3x + 5y - 7 = 0 \]
We can rewrite this in standard form by dividing the entire equation by 2:
\[ x^2 + y^2 - \frac{3}{2}x + \frac{5}{2}y - \frac{7}{2} = 0 \]

2. **Complete the Square**:
To convert the equation into standard form, we complete the square for both \(x\) and \(y\):
- For \(x\):
\[ x^2 - \frac{3}{2}x = \left(x - \frac{3}{4}\right)^2 - \frac{9}{16} \]
- For \(y\):
\[ y^2 + \frac{5}{2}y = \left(y + \frac{5}{4}\right)^2 - \frac{25}{16} \]

Substituting these back into the equation gives:
\[ \left(x - \frac{3}{4}\right)^2 + \left(y + \frac{5}{4}\right)^2 = \frac{7}{2} + \frac{9}{16} + \frac{25}{16} \]
Simplifying the right side:
\[ \frac{7}{2} = \frac{56}{16}, \quad \text{thus,} \quad \frac{56 + 9 + 25}{16} = \frac{90}{16} = \frac{45}{8} \]
So, the center of the circle is \(\left(\frac{3}{4}, -\frac{5}{4}\right)\) and the radius is \(\sqrt{\frac{45}{8}}\).

3. **Equation of the Chord of Contact**:
The chord of contact from a point \(P(h, k)\) to the circle is given by:
\[ hx + ky - \frac{3}{4}h - \frac{5}{4}k - \frac{7}{2} = 0 \]
We need to check if the line \(x + 9y - 12 = 0\) can be expressed in this form.

4. **Equate the Coefficients**:
The line \(x + 9y - 12 = 0\) can be rearranged to:
\[ 1x + 9y - 12 = 0 \]
Comparing coefficients, we have:
- \(h = 1\)
- \(k = 9\)
- \(-\frac{3}{4}h - \frac{5}{4}k - \frac{7}{2} = -12\)

Substituting \(h\) and \(k\):
\[ -\frac{3}{4}(1) - \frac{5}{4}(9) - \frac{7}{2} = -12 \]
Simplifying:
\[ -\frac{3}{4} - \frac{45}{4} - \frac{14}{4} = -12 \quad \Rightarrow \quad -\frac{62}{4} = -12 \quad \Rightarrow \quad -15.5 \neq -12 \]
Hence, the line does not satisfy the equation of the chord of contact.

5. **Conclusion**:
Since the point \(P(1, 9)\) does not lie outside the circle (as calculated), the line \(x + 9y - 12 = 0\) cannot be the chord of contact. Therefore, **Statement 1 is false**.

**Statement 2** is a general truth about the chord of contact, hence it is true.

### Final Answer:
- Statement 1: False
- Statement 2: True