+1459 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.
+1926 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! :)
+1926 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! :)
