Passing through (2, 2√3) and is inclined with the x-axis at an angle of 75°

Solution:

The slope of the line that inclines with the x-axis at an angle of 75° is m = tan 75°

m = tan (45° + 30°)

= (tan 45° + tan 30°)/(1- tan 45° tan 30°)

= (1 + 1/√3) / (1 - 1 x 1/√3)

= [(√3 + 1)/√3] / [(√3 - 1)/√3]

= (√3 + 1) / (√3 - 1)

We know that the equation of the line passing through point (x\(_0\) , y\(_0\)) , whose slope is m,

(y - y\(_0\)) = m (x - x\(_0\))

Thus, if a line passes through (2, 2√3) and is inclined with the x-axis at an angle of 75°, then the equation of the line is given as

(y - 2√3) = (√3 + 1) / (√3 - 1)  (x - 2)

(y - 2√3)(√3 - 1) = (√3 + 1)  (x - 2)

y (√3 - 1) - 2√3 (√3 - 1) = x (√3 + 1) - 2 (√3 + 1)

x (√3 + 1) - y (√3 - 1) = 2√3 + 2 - 6 + 2√3

x (√3 + 1) - y (√3 - 1) = 4√3 - 4

(√3 + 1)x - (√3 - 1)y = 4 (√3 - 1)

Hence the equation is (√3 + 1)x - (√3 - 1)y = 4 (√3 - 1)

---

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 4

Passing through (2, 2√3) and is inclined with the x-axis at an angle of 75°.

Summary:

The equation of the line which passes through (2, 2√3) and is inclined with the x-axis at an angle of 75° is (√3 + 1)x - (√3 - 1)y = 4 (√3 - 1)