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).

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The answers for part a) is given in the following link.

http://www.enotes.com/homework-help/let-u-v-two-parallel-lines-passing-through-points-446114

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)`

**Sources:**

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