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  • The angle between the tangents drawn from the origin to the circle <img alt="(x-7)^2+(y+1)^2=25" src="https://entrancecorner.oncodecogs.com/gif.latex?%28x-7%29%5E2&plus;%28y&plus;1%29%5E2%3

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

Option: 1

\pi / 3


Option: 2

\pi / 6


Option: 3

\pi / 2


Option: 4

\pi / 8


Answers (1)

best_answer

If y=m x is a tangent from the origin to the circle (x-7)^2+(y+1)^2=25, then

                                                                                 \frac{7 m-(-1)}{\sqrt{\left(m^2+1\right)}}= \pm 5 \quad \text { or } 12 m^2+7 m-12=0 .

If  m_1, m_2 are its roots, then m_1 m_2=-12 / 12=-1.

Hence the angle between the two tangents is \pi / 2,

So, (c) is correct answer. (Here origin lies on director circle of given circle)

Posted by

Ritika Harsh

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