Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, -5).
Solution:
The equation of the circle with centre (h, k) and radius r is
(x - h)2 + (y - k)2 = r2
The radius of the circle is half the length of the diameter. The diameter's endpoints are given and we use the distance formula to find the length of the diameter.
= 1/2 \(\sqrt{(7-7)^{2}+(-5-3)^{2}}\)
= 1/2 √(-8)2
= 1/2 × 8
= 4
We know that
The center of the circle is the midpoint of the diameter. Thus by using the midpoint formula, we can determine its center.
(h, k) = [(x1 + x2)/2, (y1 + y2)/2]
Substituting the values
(h, k) = [(7 + 7)/2, (3 - 5)/2]
(h, k) = (14/2, -2/2)
(h, k) = (7, -1)
Substituting the values
(x - 7)2 + (y + 1)2 = 42
Therefore, the equation of the circle is (x - 7)2 + (y + 1)2 = 42.
Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, -5).
Summary:
The equation of the circle that has a diameter with endpoints located at (7, 3) and (7, -5) is (x - 7)2 + (y + 1)2 = 42.
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