Directions: The following question contains statement - 1 (Assertion), statement - 2 (Reason), 4 choices (A), (B), (C) and (D) out of which only one is correct. Tangents are drawn from the point (17, 7) to the circle x² + y² = 169 Statement - 1 The tangents are mutually perpendicular. Because Statement - 2 The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x² + y² = 338.

The given circle equation is x squared plus y squared equals 169, giving a radius of 13; the locus of points from which mutually perpendicular tangents can be drawn to a circle is its director circle, whose equation is x squared plus y squared equals 2 times r squared. Substituting the radius gives the director circle equation as x squared plus y squared equals 338, which matches statement 2 and proves it is true. Since the point (17, 7) yields 17 squared plus 7 squared equal to 289 plus 49, which is 338, the point lies on the director circle; therefore, the tangents drawn from it are mutually perpendicular, making statement 1 true, and statement 2 is a correct explanation for statement 1.

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