+1800 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.
+1953 We have a system of equations we need to solve.
We have the system
x=4x2+y2=25
Plugging in x as 4 into the second equation, we have
16+y2=25y2=9y=±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! :)
+1953 We have a system of equations we need to solve.
We have the system
x=4x2+y2=25
Plugging in x as 4 into the second equation, we have
16+y2=25y2=9y=±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! :)
