Q.

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.               [2007]

1 Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.  
2 Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.  
3 Statement-1 is True, Statement-2 is False.  
4 Statement-1 is False, Statement-2 is True.  

Ans.

(1)

Equation of director circle of the given circle x2+y2=169 is x2+y2=2×169=338

We know that from every point on the director circle, the tangents drawn to the given circle are perpendicular to each other.

Since (17,7) lies on the director circle,

∴ The tangents from (17,7) to the given circle are mutually perpendicular.