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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

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


Option: 4

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


Answers (1)

best_answer

Equation of chord or contact of the pair of tangent from (0,0) and (\mathrm{g}, \mathrm{f}) are

\mathrm{g x+f y+c=0 \quad \ldots .(1) \text { and } \quad g x+f y+\frac{g^{2}+f^{2}+c}{2}=0\quad \ldots(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| \quad}

Posted by

vishal kumar

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