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  • The equation of the circle, which is touched by the line , has its centre on the positive direct

The equation of the circle, which is touched by the line \mathrm{y=x}, has its centre on the positive direction of the x-axis and cut off a chord of length 2 units on the line \mathrm{\sqrt{3} y=x}, is
 

Option: 1

\mathrm{x^2+y^2-4 x+2=0}

 


Option: 2

\mathrm{x^2+y^2-4 x+1=0}
 


Option: 3

\mathrm{x^2+y^2-8 x+8=0}
 


Option: 4

\mathrm{x^2+y^2-4 y+2=0}


Answers (1)

best_answer

\mathrm{O P=C P=\frac{h}{\sqrt{2}}=A C}

\mathrm{C M=h \sin 30^{\circ}=\frac{h}{2}}
From \mathrm{ACM \quad \Delta }

\mathrm{A C^2=A M^2+C M^2 }

\mathrm{ \frac{h^2}{2}=1+\frac{h^2}{4} \quad \Rightarrow \quad \frac{h^2}{4}=1 \quad \Rightarrow \quad h=2 }

\mathrm{ \text { radius }=\sqrt{2} }

\mathrm{ (x-2)^2+y^2=2 ; x^2+y^2-4 x+2=0}

Hence option 1 is correct.



 

Posted by

Deependra Verma

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