SOLUTION: Hello I'm really stuck on this question and would be very grateful if you could help me out. QUESTION:Find the points of intersection of the line y=5x+13 with the circle {{{

Question 291123: Hello
I'm really stuck on this question and would be very grateful if you could help me out.
QUESTION:Find the points of intersection of the line y=5x+13 with the circle
I'm not really sure how to approanch this question but have been attempting to solve it almost like a simultaneous equation by substitution:

This eventually gets me down to the quadratic:

simplified to
This is all probably wrong but even if I am right I don't know where to go from here...
Please help!
Thanks ever so much,
From Katie
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You're on the right track. I'll start where you left off.

Let's solve by use of the quadratic formula.

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=13, b=65, and c=78

Square 65 to get 4225

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 13 to get 26

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

Now plug each of these solutions into to find the corresponding 'y' coordinates of the intersections.

So when , then giving us the point (-2,3)

Also, when , then giving us the point (-3,-2)

So the two points of intersection are (-2,3) and (-3,-2)

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