+1297 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.
+2159
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.
I drew both on Desmos.
The intersection points are (+4, +3)
and (–4, –3)
That makes the chord AB = 6 i.e., 3 – (–3) = 6
You can also do it by substitution . . . y2 = 25 – 16
y = +3
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