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  • If  is a point on the circle whose centre is on the <img alt="x" src="https://en

If (\alpha, \beta)  is a point on the circle whose centre is on the x -axis and which touches the line \mathrm{x+y=0} at (2,-2) , then the greatest value of \alpha is

Option: 1

4-\sqrt{2}


Option: 2

6


Option: 3

4+2 \sqrt{2}


Option: 4

4+ \sqrt{2}


Answers (1)

best_answer

\mathrm{Equation\: of \: \mathrm{O} \Rightarrow(\mathrm{x}-2)^{2}+(\mathrm{y}+2)^{2}+\mathrm{k}(\mathrm{x}+\mathrm{y})=0}

use y coordinate of circle  \mathrm{=0 \Rightarrow \mathrm{k}=-4}

centre of circle \mathrm{\Rightarrow(4,0)}

\mathrm{radius =2 \sqrt{2}}

maximum value of \mathrm{\mathrm{a} \Rightarrow} co-ordinate of \mathrm{\mathrm{B}}

\mathrm{\Rightarrow \quad \mathrm{OC}+\mathrm{CB} \quad(\mathrm{CB}= radius ) \quad \Rightarrow 4+2 \sqrt{2}}

Posted by

Devendra Khairwa

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