It is known that a straight line m and a straight line L: y = 2x + 3 have the same intercept on the y-axis, and the inclination angle is twice that of L. The equation for finding a straight line m is given

It is known that a straight line m and a straight line L: y = 2x + 3 have the same intercept on the y-axis, and the inclination angle is twice that of L. The equation for finding a straight line m is given

Let the inclination angle of l be a, then Tana = 2,
Then the inclination angle of M is 2a, which is determined by the angle doubling formula: tan2a = 2tana / (1-tan & # 178; a) = - 4 / 3
So, the slope of M is k = - 4 / 3, and the intercept is 3
Therefore, the equation of line m is y = - 4x / 3 + 3
The result is: 4x + 3y-9 = 0

Given the straight line L: x + Y-2 = 0, a beam of light passing through the point P (0, √ 3 + 1) is projected onto l with an inclination angle of 120 degrees, and then the equation of the straight line where the reflected ray is located is obtained

According to the problem, there are two rays: one is 120 degrees from the positive Y axis, and the other is 120 degrees from the negative Y axis
The angle between L and Y axis is 120 degrees, the ray, Y axis and the original line intersect to form a triangle. There are two angles: the angle between ray and Y axis is 120 degrees, the angle between line and Y axis is 45 degrees, then the angle between ray and line is 15 degrees
The intersection of reflected light, Y-axis and straight line forms a triangle. There are two angles: the angle between reflected light and straight line is 15 degrees, the angle between straight line and x-axis is 45 degrees, so the angle between reflected light and x-axis is 120 degrees
The slope of the reflected ray is: tan120 = - 3
The light slope is 1 / √ 3, so the light equation is x = √ 3 / 3x + 1 + √ 3

If a straight line is drawn through the point P (1,2) and its inclination angle is twice that of the straight line L: x-y-3 = 0, then the equation of the straight line is______ ．

Let the inclination angle of the straight line l be α and α ∈ (0, π 2) ∪ (π 2, π). First, according to x-y-3 = 0, the slope of the straight line is 1, and according to the slope k = Tan α = 1, α = 45 degrees. Because the inclination angle of the straight line is 2 α = 90 degrees, the straight line is perpendicular to the X axis and passes (1, 2), so the equation of the straight line is x = 1, so the answer is x = 1