Circle And System Of Circles Question 54

Question: The equation to the tangents to the circle $ x^{2}+y^{2}=4 $ , which are parallel to $ x+2y+3=0 $ , are

[MP PET 2003]

Options:

A) $ \sqrt{13} $

B) $ \sqrt{38} $

C) $ 2\sqrt{2} $

D) $ 2\sqrt{13} $

Show Answer

Answer:

Correct Answer: A

Solution:

Length of the tangent $ =\sqrt{4^{2}+5^{2}+2\cdot 1\cdot 4+2,(-3)\cdot 5-6}=\sqrt{13} $ .