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A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

 Jun 27, 2024

Best Answer 

 #1
avatar+1230 
+1

We have a system of equations we need to solve. 

We have the system

\(x=4\\ x^2+y^2=25\)

 

Plugging in x as 4 into the second equation, we have

\(16+y^2=25\\ y^2=9\\ y= \pm 3\)

 

Thus, we find there are two ordered pairs and solutions to the equation. We have that

\((4, 3); (4, -3)\)

 

The distance between the two is just \(3-(-3) = 6\) since they share the same x value. 

 

Thus, 6 is our answer. 

 

Thanks! :)

 Jun 27, 2024
 #1
avatar+1230 
+1
Best Answer

We have a system of equations we need to solve. 

We have the system

\(x=4\\ x^2+y^2=25\)

 

Plugging in x as 4 into the second equation, we have

\(16+y^2=25\\ y^2=9\\ y= \pm 3\)

 

Thus, we find there are two ordered pairs and solutions to the equation. We have that

\((4, 3); (4, -3)\)

 

The distance between the two is just \(3-(-3) = 6\) since they share the same x value. 

 

Thus, 6 is our answer. 

 

Thanks! :)

NotThatSmart Jun 27, 2024

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