Let u and v be two parallel lines passing through the points A=(5,0) and
B=(-5,0) respectively.Let the line 4x+3y=25 meet u at P and v at Q.
a)If the length of PQ is 5 units, show that there are two possibilities for the pair of parallel lines u and v.
b)Write down the equations of all four lines determined above.
Answer only part b).
The answers for part a) is given in the following link.
According to the previous parts it is proven that there are two sets of lines for u and v.
For `m = 4/7`
`u rarr y = m(x-5) => y = 4/7(x-5)`
`v rarr y = m(x+5) => y = 4/7(x+5)`
For `m = -4/13 `
`u rarr y = m(x-5) => y = -4/13(x-5)`
`v rarr y = m(x+5) => y = -4/13(x+5)`
So the equations of the four lines are;
`y = 4/7(x-5)`
`y = 4/7(x+5)`
`y = -4/13(x-5)`
`y = -4/13(x+5)`