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Find the set of values of c, if the line \mathrm{x-2y+c} lies outside the circle \mathrm{x^2+y^2-2 x+4 y-2 c=0}

Option: 1

\mathrm{c \in[0, \infty)}


Option: 2

\mathrm{c \in(-\infty, 1]}


Option: 3

\mathrm{c \in R-\{0\}}


Option: 4

\mathrm{ c \in(-\infty, 1)}


Answers (1)

Radius of the circle \mathrm{=\sqrt{5+2 c}}. Distance of  the centre (1, –2) from the line \mathrm{|5+c| / \sqrt{5}} 

According to the given condition \mathrm{|5+c| / \sqrt{5}>\sqrt{5+2 c} \Rightarrow c} is any real number other than zero.

 

 

Posted by

Ramraj Saini

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