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)

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Answer:

Correct Answer: 12. (a)

Solution:

  1. 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.



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