The tangent and the normal lines at the point \left ( \sqrt{3} ,1\right ) to the circle x^{2}+y^{2}=4 and the x-axis from a triangle. The area of this triangle (in square units) is : 
 

    

 

 

  • Option 1)

    \frac{4}{\sqrt{3}}

  • Option 2)

    \frac{1}{3}

  • Option 3)

    \frac{2}{\sqrt{3}}

     

  • Option 4)

    \frac{1}{\sqrt{3}}

Answers (1)

x^{2}+y^{2}=4

Equation of tangent at P\left ( \sqrt{3},1 \right )

\sqrt{3}x+y\cdot 1=4                        

x-intercepts = \frac{4}{\sqrt{3}}

Area of \bigtriangleup le.

=\frac{1}{2}\times \frac{4}{\sqrt{3}}\times 1=\frac{2}{\sqrt{3}}


Option 1)

\frac{4}{\sqrt{3}}

Option 2)

\frac{1}{3}

Option 3)

\frac{2}{\sqrt{3}}

 

Option 4)

\frac{1}{\sqrt{3}}

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