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  • The angle between the tangents drawn from the origin to the circle <img alt="\mathrm{(x-7)^{2}+(y+1)^{2}=25}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28x-7%29%5E%7B2%7D&am

The angle between the tangents drawn from the origin to the circle \mathrm{(x-7)^{2}+(y+1)^{2}=25} is

Option: 1

\frac{\pi}{3}


Option: 2

\frac{\pi}{6}


Option: 3

\frac{\pi}{2}


Option: 4

\frac{\pi}{8}


Answers (1)

best_answer

Let \mathrm{y=m x} be a tangent from the origin to the circle \mathrm{(x-7)^{2}+(y+1)^{2}=5^{2}}, then

\mathrm{\frac{7 m-(-1)}{\sqrt{m^{2}+1}}= \pm 5 \Rightarrow 12 \mathrm{~m}^{2}+7 \mathrm{~m}-12=0}

Let \mathrm{\mathrm{m}_{1}} and \mathrm{\mathrm{m}_{2}} be the slope of the tangents. Then \mathrm{\mathrm{m}_{1} \mathrm{~m}_{2}=} product of the roots \mathrm{-12 / 12=-1}.

Hence, the angle between two tangents is \mathrm{\pi / 2}.

Posted by

Irshad Anwar

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