Step-by-step Solution:

1. Analyze the given circle's equation.

The equation of the circle is given as $x^2 + y^2 = 169$. This is a standard form of a circle, $x^2 + y^2 = r^2$, with its center at the origin (0, 0). The radius of the circle is $r = \sqrt{169} = 13$.

2. Evaluate Statement 2.

Statement 2: "The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2+y^2=338$".

This statement refers to the concept of the director circle. The director circle is the locus of all points from which two tangents drawn to a given circle are perpendicular to each other.

For a circle with the equation $(x-h)^2 + (y-k)^2 = r^2$, the equation of its director circle is $(x-h)^2 + (y-k)^2 = 2r^2$.

For the given circle, $x^2 + y^2 = 169$, the center is $(h, k) = (0, 0)$ and the radius is $r = 13$. Therefore, the equation of its director circle is: $x^2 + y^2 = 2r^2$ $x^2 + y^2 = 2 \times (13)^2$ $x^2 + y^2 = 2 \times 169$ $x^2 + y^2 = 338$

This matches the equation given in Statement 2. Hence, Statement 2 is True.

3. Evaluate Statement 1.

Statement 1: "The tangents are drawn from the point (17, 7) to the circle $x^2+y^2=169$. The tangents are mutually perpendicular."

For the tangents drawn from a point to a circle to be mutually perpendicular, the point must lie on the director circle of the given circle.

From Step 2, we found the equation of the director circle to be $x^2 + y^2 = 338$.

Now, we need to check if the point (17, 7) lies on this director circle. We do this by substituting $x=17$ and $y=7$ into the equation of the director circle: $x^2 + y^2 = (17)^2 + (7)^2$ $= 289 + 49$ $= 338$

Since the coordinates of the point (17, 7) satisfy the equation of the director circle ($17^2 + 7^2 = 338$), the point lies on the director circle. Therefore, the tangents drawn from (17, 7) to the circle $x^2 + y^2 = 169$ are indeed mutually perpendicular.

Hence, Statement 1 is True.

4. Determine the relationship between the two statements.

Statement 1 makes a specific claim about the tangents from the point (17, 7). Statement 2 provides the general rule or principle (the locus of points for perpendicular tangents) for the given circle.

The reason Statement 1 is true is precisely because the point (17, 7) satisfies the condition described in Statement 2. That is, the point (17, 7) lies on the director circle whose equation is given in Statement 2.

Therefore, Statement 2 is the correct explanation for Statement 1.

Conclusion:

• Statement 1 is True.
• Statement 2 is True.
• Statement 2 is a correct explanation for Statement 1.

This corresponds to option A.