SOLUTION: Do the circle x^2+y^2=16 and the line 5x-y=20 have any points in common? If so, what are they? Thank you in advanced.

Question 986148: Do the circle x^2+y^2=16 and the line 5x-y=20 have any points in common?
If so, what are they?
Thank you in advanced.
Found 2 solutions by Cromlix, solver91311:
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Circle
x^2 + y^2 = 16
Line
5x - y = 20
-y = -5x + 20
y = 5x - 20
Substitute y = 5x - 20
in x^2 + y^2 = 16
x^2 + (5x - 20)^2 = 16
x^2 + 25x^2 - 200x + 400 = 16
Collect like terms
26x^2 - 200x + 384 = 0
Divide throughout by 2
13x^2 - 100x + 192 = 0
(13x - 48)(x - 4) = 0
13x - 48 = 0
x = 48/13
x - 4 = 0
x = 4
Substituting in y = 5x - 20
x = 48/13
y = 5(48/13) - 20
y = 240/13 - 260/13 (20)
y = - 20/13
(48/13, -20/13)
x = 4
y = 5(4) - 20
y = 20 - 20
y = 0
(4,0)
Hope this helps :-)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Solve both of your equations for .

In order for there to be a point in common, you need to find a value of that makes the two values the same, so solve:

I'll get you started. First square both sides:

Collect like terms in the LHS:

Solve the quadratic. Hint: It factors. Take 2 out first.

John

My calculator said it, I believe it, that settles it

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