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Question

A line through the point A(2, 0), which makes an angle of 30 with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15. The equation of the straight line in the new position is


A

(23)xy4+23=0

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B

(23)x+y4+23=0

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C

(23)xy+4+23=0

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D

(23)x9y+4+23=0

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Solution

The correct option is A

(23)xy4+23=0


Let AB be the initial position of the line and AC be its new position.

Slope of the line

AC=tan 15=(23)

Equation of the line AC is

(y0)=(23)(x2)or y=(23)x4+23or (23)xy4+23=0


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