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  • If is the origin and <img alt="\mathrm{OA}, \mathrm{OB}" src="https://entrancecorner.oncodecogs.com/g

If \mathrm{O} is the origin and \mathrm{OA}, \mathrm{OB} are the tangents from the origin to the circle \mathrm{x}^{2}+\mathrm{y}^{2}-4 \mathrm{x}+2 \mathrm{y}+4=0, the circumcentre of the triangle \mathrm{OAB} is

Option: 1

\left(1,-\frac{1}{2}\right)


Option: 2

\left(1, \frac{1}{2}\right)


Option: 3

\left(-1, \frac{1}{2}\right)


Option: 4

\left(-1,-\frac{1}{2}\right)


Answers (1)

best_answer

Equation of chord of contact \mathrm{AB}, is \mathrm{2 x-y-4=0}

 Required Equation of circle is
 \mathrm{x^{2}+y^{2}-4 x+2 y+4+\lambda(2 x-y-4)=0}\quad \cdots(1)

(1) passes through (0,0) \Rightarrow \ldots . \lambda=1

Equation of circumcircle is \mathrm{x^{2}+y^{2}-2 x+y=0}
 

Posted by

Gautam harsolia

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