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  • Equation of a circle  <img alt="\mathrm{\mathrm{S}(\mathrm{x}, \mathrm{y})=0,(\mathrm{~S}(2,3)=16)}" src="/latex-image/?%5Cmathrm%7B%5Cmathrm%7BS%7D%28%5Cmathrm%7Bx%7D%2C%20%5Cmathrm%7By%7D%29

Equation of a circle  \mathrm{\mathrm{S}(\mathrm{x}, \mathrm{y})=0,(\mathrm{~S}(2,3)=16)} which touches the line \mathrm{3 x+4 y-7=0 \text { at }(1,1)} is given

by

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

none of these


Answers (1)

best_answer

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

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

Since  \mathrm{\mathrm{S}(2,3)=16 \Rightarrow \lambda=1} , so required circle will be

\mathrm{x^2+y^2+x+2 y-5=0 .}

Hence (a) is correct answer.

Posted by

Devendra Khairwa

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