Question

Find the equation of straight line which passes through the point (4, 5) and make similar angles with lines 3x = 4y + 7 and 5y = 12x + 6

Answer 1

Equation of line passing through the point (4, 5)

y – 5 = m₁ (x – 4) …(i)

Given line 3x = 4y + 7

⇒ 4y = 3x – 7

⇒ y = 3/4 x – 7/4 …(ii)

Comparing with y = m₂ x + c₂
m₂ = 3/4

other line 5y = 12x + 6

⇒ y = 12/5 x + 6/5 …(iii)

Comparing with y = m₃x + c₃

According to question m₃ = 12/5

Angle between line (i) and (ii) = Angle between line (i) and (iii)