Missing one solution

[Ana.stasia]

Determine the equation of a circle tangent to the lines 3x - 4y + 35 = 0 and 4x + 3y - 20 = 0, and its center is at the point C (p, 1)

I managed to solve it and get a correct solution. However, the book also has another solution and I am not sure where I went wrong to not get that one.

 

[lev888]

After taking the square root of both sides of an equation you should have 2 branches: left side = right side and left side = -(right side).

 

[Ana.stasia]

After taking the square root of both sides of an equation you should have 2 branches: left side = right side and left side = -(right side).

I do that for both cases (first page, left and right from the line in the middle), so i did what you said in both cases, however, i still got the same result. Maybe I am supposed to only do it in one case? If so which one?

 

[lev888]

Try combining the positive=positive branch on the left with positive=negative branch on the right and vice versa.

 

[Ana.stasia]

Try combining the positive=positive branch on the left with positive=negative branch on the right and vice versa.

I did so and got what I assume is the correct solution. I say assume because there are some differences, but I believe there was a typo in the book. See what I mean in the picture. Could you give me an explanation on why I got a correct answer like this? It feels like I am memorizing this problem rather than learning from it.

 

[lev888]

Could you give me an explanation on why I got a correct answer like this?

If you are referring to my last suggestion: imagine the first equation didn't require taking the square root. What would you do with the positive=negative branch of the second equation? You would combine it with the first equation. Wouldn't it still make sense to do it when the first equation has its own positive=negative branch?

 

[Dr.Peterson]

I did so and got what I assume is the correct solution. I say assume because there are some differences, but I believe there was a typo in the book. See what I mean in the picture. Could you give me an explanation on why I got a correct answer like this? It feels like I am memorizing this problem rather than learning from it.

It looks like the two radii are indeed respectively 5 and 35, not 39:

 

[lex]

@Ana.stasia
Re. your very first post.

 

[Ana.stasia]

7

It looks like the two radii are indeed respectively 5 and 35, not 39:
View attachment 25767

Thank you.