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  • Equation of a circle  which touches the line <img alt="3 x+4

Equation of a circle S(x, y)=0, S(2,3)=16  which touches the line 3 x+4 y-7=0 at (1,1) is given by

Option: 1

x^{2}+y^{2}+x+2 y-5=0


Option: 2

x^{2}+y^{2}+2 x+2 y-6=0


Option: 3

x^{2}+y^{2}+4 x-6 y=0


Option: 4

none of these

 


Answers (1)

best_answer

Any circle which touches 3 x+4 y-7=0 at (1,1) will be of the form

\mathrm{S}(\mathrm{x}, \mathrm{y})(\mathrm{x}-1)^{2}+(\mathrm{y}-1)^{2}+\lambda(3 \mathrm{x}+4 \mathrm{y}-7)=0
\text{Since} \: S(2,3)=16

\Rightarrow \lambda=1, so required circle will be
\mathrm{x} 2+\mathrm{y} 2+\mathrm{x}+2 \mathrm{y}-5=0

Hence (a) is the correct answer.

 

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chirag

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