Question

Find the joint equation of pair of lines passing through A(2,3)& makes angleof 30^0 with Y-axis

Answer 1

Step-by-step explanation:

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Answer 2

The equations of the two lines passing through A(2,3) and making an angle of 30 degrees with the y-axis are:

y = (1/√3)x + (3 - 2/√3)

y = (1/√3)x + (3 - 2/√3)

To find the equation of lines passing through point A(2,3) and making an angle of 30 degrees with the y-axis, we first note that the angle between a line and the y-axis is equal to the angle between the line and the positive x-axis.

Let the two lines passing through A(2,3) be represented by the equations y = mx + c1 and y = mx + c2, where m is the slope of the lines, and c1 and c2 are the y-intercepts.

Since the lines make an angle of 30 degrees with the y-axis, the slope of the lines must be the tangent of 30 degrees, which is 1/√3. Therefore, we have:

m = 1/√3

Now, we can use the fact that the lines pass through A(2,3) to find the values of c1 and c2. Substituting the coordinates of A into the equations of the lines, we get:

3 = (1/√3)*2 + c1

3 = (1/√3)*2 + c2

Simplifying these equations, we get:

c1 = 3 - (2/√3)

c2 = 3 - (2/√3)

Therefore, the equations of the two lines passing through A(2,3) and making an angle of 30 degrees with the y-axis are:

y = (1/√3)x + (3 - 2/√3)

y = (1/√3)x + (3 - 2/√3)

which can be written as:

y = (1/√3)x + 3√3 - 2

y = (1/√3)x + 3√3 - 2

Alternatively, we can write the joint equation of these two lines as:

y = (1/√3)x + 3√3 - 2 ± k√3x

where k is any non-zero integer, and the ± sign indicates that the two lines have opposite y-intercepts.

For such more questions on joint equation,

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