Perpendicular Tangents from a Point to a Circle

To determine the validity of the statements, we analyze the properties of the given circle and its director circle:

1. Analysis of Statement-2:
   The given circle is:
   $x^2 + y^2 = 169$
   The radius of the circle is $r = \sqrt{169} = 13$.

   The locus of points from which mutually perpendicular tangents can be drawn to a circle is known as its director circle.
   For a circle of radius $r$ centered at the origin, the equation of its director circle is given by:
   $x^2 + y^2 = 2r^2$
   Substituting $r^2 = 169$:
   $x^2 + y^2 = 2(169) = 338$
   Therefore, the locus of points from which mutually perpendicular tangents can be drawn to the circle is indeed $x^2 + y^2 = 338$.
   Hence, Statement-2 is True.

2. Analysis of Statement-1:
   We are given the point $P(17, 7)$. Let us check if this point lies on the director circle found above:
   $x^2 + y^2 = 17^2 + 7^2 = 289 + 49 = 338$
   Since the coordinates of the point $(17, 7)$ satisfy the equation of the director circle, the tangents drawn from this point to the given circle $x^2 + y^2 = 169$ must be mutually perpendicular.
   Hence, Statement-1 is True.

3. Conclusion:
   Statement-2 correctly defines the director circle, which is the direct mathematical reason that the tangents drawn from $(17, 7)$ are mutually perpendicular. Therefore, Statement-2 is the correct explanation for Statement-1.

Thus, the correct choice is A.