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  • The point whose chord of contact with respect to the circle <img alt="\mathrm{x^2+y^2-4 x=0 \: is\: x+4 y-6=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2

The point whose chord of contact with respect to the circle \mathrm{x^2+y^2-4 x=0 \: is\: x+4 y-6=0} is
 

Option: 1

(3,4)
 


Option: 2

(1,5)
 


Option: 3

(1,-1)

 


Option: 4

None of these


Answers (1)

best_answer

Let point be \mathrm{(h, k)}

Equation of chord of contact is

\mathrm{ h x+k y-2(x+h)=0 }

\mathrm{(h-2) x+k y-2 h=0 }          ............(1)

\mathrm{ x+4 y-6=0}

Equation (1) and (2) represent same line

\mathrm{ \frac{(\mathrm{h}-2)}{1}=\frac{\mathrm{k}}{4}=\frac{-2 \mathrm{~h}}{-6} }

\mathrm{ \Rightarrow \mathrm{h}=3, \mathrm{k}=4}

Hence option 1 is correct.



 

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