Write the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8).
a. (x - 4)2 + (y - 1)2 = 25
b.(x - 1)2 + (y - 4)2 = 25
c. (x - 1)2 + (y - 4)2 = 5
d.(x + 1)2 + (y + 4)2 = 25

B) (x - 1)² + (y - 4)² = 25.

Step-by-step explanation:

Given : A circle with a center at (1, 4) where a point on the circle is (4, 8).

To find : Write the equation of a circle.

Solution : We have given that center (1 ,4)

A point on a circle (4 ,8).

Distance between center and point on circle is called diameter .

Distance formula : .

Diameter =  .

Diameter =  .

Diameter =  .

Diameter =  .

Diameter = 5.

Radius = 2.5

Equation of center = (x - h)² + (y - k)² = r².

Where , (h , k) in coordinates of center and r is radius.

Equation of circle :  (x - 1)² + (y - 4)² = 5².

(x - 1)² + (y - 4)² = 25.

Therefore, B) (x - 1)² + (y - 4)² = 25.

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step-by-step explanation: