Question

Find the joint equation of the lines which pass through the point $(4, - 3)$ and are parallel to the lines $x = 1$ and $y = 5$.

Answer 1

Hint: We will make a diagram of $x = 1$ and $y = 5$.Further Joint equation of lines pass through the point and parallel to x and y. Then we will put the point $(4, - 3)$ to make a joint equation of line.


Complete step by step solution:

Line parallel to $x = 1$
$x = {C_1}$
Line parallel to $y = 5$
$y = {C_2}$
Line passing through $(4, - 3)$
$x = 4,\,\,\,y = - 3$
x - 4 = 0 & y + 3 = 0
Joint equation of lines $x = 4\,and\,y = 3\,is\,(x - 4)\,(y + 3) = \,0$
$xy + 3x - 4y - 12 = 0$
Is the joint equation of line passing through $(4, - 3)$and parallel to $x = 1\,and\,x = 5$


Note: Students must know that when we will draw a diagram of $x = 1$ then in this equation of line the value of $y = 0$ and this line will parallel to the y-axis. And we will draw a diagram of $y = 5$ then in this equation of line the value of $x = 0$ and this line will parallel to the x-axis.