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What is the equation of the tangent to circle x^2+y^2=16 at a point with parameter \alpha = \frac{\pi }{3}?

Option: 1

\sqrt3x+y= 8


Option: 2

\sqrt3x-y= 8


Option: 3

x+\sqrt3y= 8


Option: 4

x-\sqrt3y= 8


Answers (1)

best_answer

As we learnt

Equation of tangent in parametric form

x\cos \alpha +y\sin \alpha = a is the tangent a point \left ( a\cos \alpha ,a\sin \alpha \right ) to x^{2}+y^{2}=a^{2}

 

Now,

Here, \alpha = \frac{\pi }{3}\: \: and\: \: a=4

Thus equation is 

x\cos \frac{\pi }{3} +y\sin \frac{\pi }{3} = 4

x+\sqrt3y=8

Posted by

Devendra Khairwa

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