Question

Tangents are drawn from the point $(17,7)$ to the circle $x^{2}+y^{2}=169$
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 $x^{2}+y^{2}=338$.

• 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 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

Answer: (A)

The given circle is
$x^{2}+y^{2}=169$
The equation of its director circle is
$x^{2}+y^{2}=338$
Since point $(17,7)$ satisfy the equation of director circle, the tangents, which are drawn from the point $(17,7)$ are mutually perpendicular and the locus of the perpendicular tangents is the director circle.
Hence, both statements are true and Statement-$2$ explains Statement- $1 .$