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  • The distance between the chords of contact of tangents to the circle ; <img alt="\mathrm{x^{2}+y^{2}+2 g x+2 f y+c=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E%7B2%7Da

The distance between the chords of contact of tangents to the circle ; \mathrm{x^{2}+y^{2}+2 g x+2 f y+c=0} from the origin & the point \mathrm{(\mathrm{g}, \mathrm{f})} is :

Option: 1

\sqrt{\mathrm{g}^{2}+\mathrm{f}^{2}}


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

Equation of chord or contact are  \quad \mathrm{gx}+\mathrm{fy}+\mathrm{c}=0\quad \cdots{1}
                                                     & \mathrm{\quad 2 g x+2 f y+\frac{g^{2}+f^{2}+c}{2}=0} \cdots (2)

These lines are parallel

\mathrm{hence \: distance =\left|\frac{\mathrm{c}-\frac{\mathrm{g}^{2}+\mathrm{f}^{2}+\mathrm{c}}{2}}{\sqrt{\mathrm{g}^{2}+\mathrm{f}^{2}}}\right|

Posted by

Sumit Saini

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