Given: circle O with diameter CD C(5,4) D(3,2) create a equation if the circle?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the equation of a circle with endpoints of a diameter, we first need to find the center of the circle, which is the midpoint of the diameter. Then, we can use the distance formula to find the radius of the circle. Once we have the center and the radius, we can write the standard equation of the circle, which is ((x  h)^2 + (y  k)^2 = r^2), where ((h, k)) is the center of the circle and (r) is the radius.

Find the midpoint of the diameter CD: [h = \frac{x_1 + x_2}{2}, \quad k = \frac{y_1 + y_2}{2}] [h = \frac{5 + 3}{2} = 1, \quad k = \frac{4  2}{2} = 1] So, the center of the circle is (1, 1).

Calculate the radius using the distance formula between points C and D: [r = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2}] [r = \sqrt{(3  (5))^2 + (2  4)^2} = \sqrt{8^2 + (6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10]

Substitute the center and radius into the standard equation of a circle: ((x + 1)^2 + (y  1)^2 = 10^2)
Therefore, the equation of the circle is ((x + 1)^2 + (y  1)^2 = 100).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 A triangle has corners at #(2 , 8 )#, #(5 ,7 )#, and #(3 ,1 )#. What is the radius of the triangle's inscribed circle?
 A circle's center is at #(5 ,4 )# and it passes through #(1 ,4 )#. What is the length of an arc covering #(2pi ) /3 # radians on the circle?
 A circle's center is at #(7 ,5 )# and it passes through #(5 ,4 )#. What is the length of an arc covering #(5pi ) /3 # radians on the circle?
 A circle has a center at #(3 ,1 )# and passes through #(2 ,1 )#. What is the length of an arc covering #pi/8# radians on the circle?
 A circle has a center that falls on the line #y = 7/9x +5 # and passes through # ( 7 ,3 )# and #(5 ,1 )#. What is the equation of the circle?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7