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I am doing "Equations" in Algebra 2 in Khanacdemy and stumbled on this problem:

Find all the Intersecting points of a circle and a line:

Circle equation   :$$(x-1)^2+(y-1)^2=1$$

Line equation     :$$y=2x+1$$

And I tried the following but I am not sure if it is correct:

$$Since\ y=2x+1,\ we\ plug\ it\ into\ the\ circle\ equation. \\ (line\ 1): (x-1)^2+(y-1)^2=1 \\ (line\ 2): (x-1)^2+(2x+1-1)^2=1 \\ (line\ 3): (x-1)^2+(2x)^2=1 \\ (line\ 4): x^2-2x+1+4x^2=1 \\ (line\ 5): 5x^2-2x+1=1 \\ (line\ 6): 5x^2-2x=0 \\ (line\ 7): x(5x-2)=0 \\ x=0 \\ x=2/5$$

From there, I do not know what to do...

It would be great if you could help me from there and tell me if I am on the right path.

-Tommarvoloriddle

EDITS:

Circle and line:

Parabola and line:

No solution:

Aug 14, 2019
edited by tommarvoloriddle  Aug 14, 2019
edited by tommarvoloriddle  Aug 14, 2019
edited by tommarvoloriddle  Aug 14, 2019
edited by tommarvoloriddle  Aug 14, 2019
edited by tommarvoloriddle  Aug 14, 2019

#1
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I am not sure on this one but I would just plug back in the original equations.

Aug 14, 2019
#2
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Plug what in?

tommarvoloriddle  Aug 14, 2019
#3
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Find all the Intersecting points of a circle and a line:
Circle equation   :  ($$x-1)^2+(y-1)^2=1$$
Line equation     :  $$y=2x+1$$

$$\begin{array}{|rclrcl|} \hline \mathbf{x_1} &=& \mathbf{0} \\ && & y_1 &=& 2x_1+1 \\ && & y_1 &=& 2\cdot 0 +1 \\ && &\mathbf{ y_1} &=& \mathbf{ 1} \\\\ \mathbf{x_2} &=& \mathbf{0.4} \\ && & y_2 &=& 2x_2+1 \\ && & y_2 &=& 2\cdot 0.4 +1 \\ && &\mathbf{ y_2} &=& \mathbf{ 1.8 } \\ \hline \end{array}$$

The two Intersecting points of a circle and a line are: $$\mathbf{(0,\ 1)}$$ and $$\mathbf{(0.4,\ 1.8)}$$ Aug 14, 2019
#4
+1

Does it matter decimals or fractions?

tommarvoloriddle  Aug 15, 2019