Question

what is the length of the chord? round to the neatest tenth.

Answer 1

Find when that circle intersects with that vertical line.

Answer 2

You already know the x of the intersection of those two points.

Answer 3

Every point that lines on that line has (x=2,for whatever y)

Answer 4

Replace the x=2 in your circle equation and solve it for y.

Answer 5

2^2+y^2=25

like that ?

Answer 6

Yep now solve for y

Answer 7

4+y^2=25
-4 -4
y^2 =21
\[\sqrt y^2=\sqrt21\]
y=4.58

Answer 8

Now since you want to know the length of the chord, just find the distance between those two points using the distance formula.
\[d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \]