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  • The distance between the chords of contact of the tangent to the circle <img alt="x^2+y^2+2 g x+2 f y+c=0" src="https://entrancecorner.oncodecogs.com/gif.latex?x%5E2&plus;y%5E2&plus;2%20g%2

The distance between the chords of contact of the tangent to the circle x^2+y^2+2 g x+2 f y+c=0 from the origin and the point (g, f) is

Option: 1

g^2+f^2


Option: 2

\frac{1}{2}\left(g^2+f^2+c\right)


Option: 3

\frac{g^2+f^2+c}{2 \sqrt{g^2+f^2}}


Option: 4

\frac{g^2+f^2-c}{2 \sqrt{g^2+f^2}}


Answers (1)

best_answer

Equations of the chords of contact of the tangents from origin (0,0)and the point (g, f) on the given circle are

0 . x+0 . y+g(x+0)+f(y+0)+c=0

or  g x+f y+c=0;                           ...(i)

and  g x+f y+g(x+g)+f(y+f)+c=0

or  g x+f y+\frac{1}{2}\left(g^2+f^2+c\right)=0             ...(ii)

Obviously, (i) and (ii) are parallel.

\therefore \quad Distance between these two chords

=\frac{\frac{1}{2}\left(g^2+f^2+c\right)-c}{\sqrt{\left(g^2+f^2\right)}}=\frac{g^2+f^2-c}{2 \sqrt{\left(g^2+f^2\right)}} .

\therefore \quad \text { (d) }

Posted by

shivangi.bhatnagar

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