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  • The tangents drawn from  the   origin to the  circle   <img alt="\mathrm{x^2+y^2+2 g x+2 f y+f^2=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathr

The tangents drawn from  the   origin to the  circle  

\mathrm{x^2+y^2+2 g x+2 f y+f^2=0}   are  perpendicular  if

Option: 1

 g = 3f 


Option: 2

g = -f


Option: 3

 g = 2f


Option: 4

2g = f


Answers (1)

best_answer

Radius of the given circle  = |g| .  For perpendicular tangents  origin  should  lie  on the  director   circle, i.e.  distance  of   origin   from  the  centre  of the   given  circle  =

\mathrm{\begin{aligned} & |g| \sqrt{2} \\ & \Rightarrow g^2+f^2=2 g^2 \Rightarrow g= \pm f . \end{aligned}}

Posted by

Irshad Anwar

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