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  • Tangent OP and OQ are  drawn from the origin O to the circle <img alt="\mathrm{x^2+y^2+2 g x+2 f y+c=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&pl

Tangent OP and OQ are  drawn from the origin O to the circle \mathrm{x^2+y^2+2 g x+2 f y+c=0} Then the equation of the circumcircle of the triangle OPQ is \mathrm{x^2+y^2+g x+f y+k=0} where k=

Option: 1

C


Option: 2

\frac{C}{2}


Option: 3

2C


Option: 4

0


Answers (1)

best_answer

The equation of chord of contact PQ is 

\mathrm{x \cdot 0+y \cdot 0+g(x+0)+f(y+0)+c=0 \Rightarrow \quad g x+f y+c=0}    (1)

The equation of circle passing through the intersection of given circle

\mathrm{x^2+y^2+2 g x+2 f y+c=0}

and the chord (1) is

\mathrm{x^2+y^2+2 g x+2 f y+c+\lambda(g x+f y+c)=0} ---(2)

It passes through O(0, 0)

\mathrm{\therefore 0+0+0+0+c+\lambda(0+0+c)=0 \Rightarrow \lambda=-1

Putting this value in Equation (2), the equation of required circle is 

\mathrm{x^2+y^2+g x+f y=0}

 

 

 

 

 

Posted by

shivangi.shekhar

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