Consider the following statements in respect of the line passing through origin and inclining at an angle of 75^{\circ} with the positive direction of x-axis : 1. The line passes through the point (1,\frac{1}{2-\sqrt{3}}) 2. The line entirely lies in first and third quadrants. Which of the statements given above is/are correct?

Explanation

The slope of the line is m = \tan 75^{\circ} = 2+\sqrt{3}. Its equation is y = (2+\sqrt{3})x. For statement 1, plugging in x=1 gives y = 2+\sqrt{3}. Since \frac{1}{2-\sqrt{3}} = 2+\sqrt{3}, the point lies on the line. For statement 2, since the line passes through the origin and has a positive slope, it lies entirely in the first and third quadrants. Both statements are correct.

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