Question

Find the joint equation of the pair of lies through the origin and making equilateral triangle
with the line x = 3. ​

Answer 1

Step-by-step explanation:

Given Find the joint equation of the pair of lies through the origin and making equilateral triangle with the line x = 3  

• Now we have the y coordinate of the graph. So there is a line x = 3. Also we neded to make an equilateral triangle in the graph. So the given angle is 60 degree and other angle is 30 degree.
• Now slope of one of the line is tan 30 degree and the other angle is tan (- 30) degree.
• So we have p1 = tan 30 = 1/√3
•               And p2 = tan (- 30) = - 1/√3√
• Now equation of lines can be written as y = 1/√3 x
•                                                            Or x - √3 y = 0
•                                                Also y = - 1/√3 x
•                                                     Or x + √3 y = 0
• Now writing both the equations combined together we get
•                                                (x + √3 y) (x - √3 y) = 0
• This is in the form of (a + b)(a – b) = a^2 – b^2
•                                                          = x^2 – (√3 y)^2
•                                                       = x^2 – 3y^2 = 0 is the required equation.

Reference link will be

https://brainly.in/question/17529251