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  • A line which is parallel to is rotated about the point <img alt="\mathrm{(2,0)}" src="https://e

A line which is parallel to \mathrm{y=x} is rotated about the point \mathrm{(2,0)} through angle \mathrm{15^{\circ}} anticlockwise direction, then y intercept of the line passing through the point of intersection new line with \mathrm{\mathrm{y}=\mathrm{x}} and at right angle to new line, is

Option: 1

2+\sqrt{3}


Option: 2

2+2 \sqrt{3}


Option: 3

4+2 \sqrt{3}


Option: 4

2-3 \sqrt{3}


Answers (1)

best_answer

\mathrm{y}-0 \sqrt{3}(\mathrm{x}-2) it intersect \mathrm{y}=\mathrm{x}

\Rightarrow \mathrm{x}=\frac{2 \sqrt{3}}{\sqrt{3}-1}


\mathrm{So \: \mathrm{P}\: is \: \left(\frac{2 \sqrt{3}}{\sqrt{3}-1}, \frac{2 \sqrt{3}}{\sqrt{3}-1}\right)}
So required line is
\mathrm{y}-\frac{2 \sqrt{3}}{\sqrt{3}-1}=-\frac{1}{\sqrt{3}}\left(\frac{\mathrm{x}-2 \sqrt{3}}{\sqrt{3}-1}\right)

it intersect \mathrm{y}-axis at \mathrm{x}=0
\mathrm{y}=\frac{2 \sqrt{3}}{\sqrt{3}-1}\left(1+\frac{1}{\sqrt{3}}\right)=4+2 \sqrt{3}
 

Posted by

Anam Khan

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