Circle 3 Question 12
12. Tangents are drawn from the point $(17,7)$ to the circle $x^{2}+y^{2}=169$.
Statement I The tangents are mutually perpendicular. because
Statement II The locus of the points from which a mutually perpendicular tangents can be drawn to the given circle is $x^{2}+y^{2}=338$.
$(2007,3 M)$
(a) Statement I is true, Statement II is true; Statement II is correct explanation of Statement I
(b) Statement I is true, Statement II is true, Statement II is not correct explanation of Statement I.
(c) Statement I is true, Statement II is false.
(d) Statement I is false, Statement II is true.
Passage Based Problems
Passage 1
A tangent $P T$ is drawn to the circle $x^{2}+y^{2}=4$ at the point $P(\sqrt{3}, 1)$. A straight line $L$, perpendicular to $PT$ is a tangent to the circle $(x-3)^{2}+y^{2}=1$.
(2012)
Show Answer
Answer:
Correct Answer: 12. (a)
Solution:
- As locus of point of intersection for perpendicular tangents is directors circle.
$$ \text { i.e. } x^{2}+y^{2}=2 r^{2} $$
Here, $(17,7)$ lie on directors circle $x^{2}+y^{2}=338$
$\Rightarrow$ Tangents are perpendicular.
