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Solution


Q.

A line passing through the point A(9, 0) makes an angle of 30° with the positive direction of x-axis. If this line is rotated about A through an angle of 15° in the clockwise direction, then its equations in the new position is          [2024]
1 x3+2+y=9  
2 y3-2+x=9  
3 x3-2+y=9  
4 y3+2+x=9  

Ans.

(2)

Let l be the line passing through point A(9, 0) making angle 30° with x-axis.

Line is rotated clockwise by 15° then l' is the new position of line where it make 15° angle with x-axis.

So, equation of line passing through (9, 0) and making angle 15° with x-axis is (y – 0) = tan 15° (x – 9)

⇒   y = tan (45° – 30°)(x – 9) = (tan 45° – tan 30°1 + tan 45° · tan 30°) (x – 9)

⇒   y = (2 – 3) (x – 9)

⇒   y2 – 3 = x – 9   ⇒   y3 – 2 + x = 9