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 Options: A . &nbsp(2−√3)x−y−4+2√3=0 B . &nbsp(2−√3)x+y−4+2√3=0 C . &nbsp(2−√3)x−y+4+2√3=0 D . &nbsp(2−√3)x−9y+4+2√3=0

A line through the point A(2, 0), which makes an angle of 30∘ with the positiv

Question

A line through the point A(2, 0), which makes an angle of

30^{\circ}

with the positive direction of x-axis is rotated about A in clockwise direction through an angle

15^{\circ}

. The equation of the straight line in the new position is

Options:

A . (2−√3)x−y−4+2√3=0

B . (2−√3)x+y−4+2√3=0

C . (2−√3)x−y+4+2√3=0

D . (2−√3)x−9y+4+2√3=0

Answer: Option A
:
A
Let AB be the initial position of the line and AC be its new position.
Slope of the line

A C = t a n 15^{\circ} = (2 - \sqrt{3})

∴

Equation of the line AC is

(y - 0) = (2 - \sqrt{3}) (x - 2) o r y = (2 - \sqrt{3}) x - 4 + 2 \sqrt{3} o r (2 - \sqrt{3}) x - y - 4 + 2 \sqrt{3} = 0

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