Question

Find the equation of the straight line which passes through the point (1, 2) and makes such
3
an angle with the positive direction of x-axis whose sine is
5
thishtlinerassing through (3-2) and making an angle of 60​

Answer 1

Question -> Find the equation of the straight line which passes through the point (1, 2) and makes such an angle with the positive direction of x – axis whose sine is 3/5.

Solution : an unknown line passing through the point (1,2) makes an angle with the positive direction of x - axis whose sine is 3/5.

I.e., Sine = 3/5

So, tangent = 3/√(5² - 3²) = 3/4

We know, slope of line is tangent of angle made by the line with the positive direction of x-axis.

So, slope of line, m = 3/4

Now equation of line passing through (1,2) is given by, (y - 2) = 3/4(x - 1)

⇒4(y - 2) = 3(x - 1)

⇒4y - 8 = 3x - 3

⇒3x - 4y + 5 = 0

Therefore the equation of unknown line is (3x - 4y + 5) = 0