Find the equation of a circle which diameter has the end point A (5, 4), B (7,4 ).
the midpoint of the diameter is the center of the circle: (6,4)
The radius is half the diameter: 1
(x-6)^2 + (y-4)^2 = 1
To find the equation of a circle given the coordinates of two endpoints of its diameter, we need to find the center and radius of the circle.
1. Find the center:
The center of the circle is the midpoint of the diameter. To find the midpoint, use the formula:
midpoint_x = (x1 + x2) / 2
midpoint_y = (y1 + y2) / 2
For the given endpoints A (5, 4) and B (7, 4):
midpoint_x = (5 + 7) / 2 = 12 / 2 = 6
midpoint_y = (4 + 4) / 2 = 8 / 2 = 4
So, the center of the circle is C(6, 4).
2. Find the radius:
The radius is half the length of the diameter. Use the distance formula to calculate the distance between the endpoints A and B:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For A (5, 4) and B (7, 4):
distance = sqrt((7 - 5)^2 + (4 - 4)^2)
= sqrt(2^2 + 0^2)
= sqrt(4)
= 2
Therefore, the radius of the circle is 2.
3. Write the equation of the circle:
The equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values we found earlier:
(x - 6)^2 + (y - 4)^2 = 2^2
The equation of the circle with diameter endpoints A(5, 4) and B(7, 4) is:
(x - 6)^2 + (y - 4)^2 = 4
Steve got it but it did nt reach quarter of d workings
Correct steve
X²+Y² -12x -8y -53 =0
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No the answer is
X^2 + y^2 - r^2 - 12x - 8y + 52 = 0
The answer is
X^2 + y^2 - r^2 - 12x - 8y + 52 = 0