Question

Tangents are drawn from the point (17, 7) to the circle `x^2+y^2=169`, Statement I The tangents are mutually perpendicular Statement, lls The locus of the points frorn which mutually perpendicular tangents can be drawn to the given circle is `x^2 +y^2=338` (a) Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statementl (b( Statement I is correct, Statement I| is correct Statement II is not a correct explanation for Statementl (c)Statement I is correct, Statement II is incorrect (d) Statement I is incorrect, Statement II is correct
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.

Answer 1

Correct Answer - A
The locus of the points from which mutually perpendicular tangents can be drawn to the circle `x^(2)+y^(2)=a^(2)` is the circle `x^(2)+y^(2)=2a^(2)`. The circle `x^(2)+y^(2)=2a^(2)` is known as the director circle of `x^(2)+y^(2)=a^(2)`. Thus, if tangents are drawn from any point on the direction circle to the given circle, then the tangents are mutually perpendicular. Hence statement-1 and 2 are true and statement-2 is a correct explanation for statement-1.