A chord of a circle is a line segment whose endpoints are on the circle. Find the length of the common chord of the two circles whose equations are #x^2 + y^2 =4# and #x^2 +y^2 -6x +2 = 0#?
1 Answer
Explanation:
Here we have equations of two circles.
Circle [A}:
Circle [B]:
To find the coordinates of the common chord we need to find the points of intersection of the [A] and [B]. i.e where equation [A] equals equation [B]
NB: In this special case we can replace
Thus:
From [A}
Hence our points of intersection and hence the endpoint of the common chord are
To find the length between these two points we use the formula:
Plugging in values of
Chord length
We can see the points of intersection and deduce the length of the common chord graphically below:
graph{(x^2+y^2-4)(x^2+y^2-6x+2)=0 [-6.243, 6.243, -3.12, 3.123]}