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  • The tangents drawn from the origin to the circle <img alt="\mathrm{x^2+y^2+2 q x+2 f y+f^2=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2&plus;2%

The tangents drawn from the origin to the circle \mathrm{x^2+y^2+2 q x+2 f y+f^2=0} are  perpendicular  if

Option: 1

 g = f

 


Option: 2

g =1 -f 

 


Option: 3

g = 2f 


Option: 4

2g = f


Answers (1)

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{=|g| \sqrt{2} \Rightarrow g^{2}+f^{2}=2g^{2}\Rightarrow g=\pm f}

 

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Kshitij

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