Which is an equation of a circle with center (5, 0) that passes through the point (1, 1)?

Answer Choices:

A. \((x - 1)^2 + (y - 1)^2 = 17\)

B. \((x + 5)^2 + y^2 = 17\)

C. \((x + 5)^2 + y^2 = 24\)

D. \((x - 5)^2 + y^2 = 17\)

a) first we will calculate the distance between center and given point because this is the radius of circle:
d = ( 1 − 5 ) 2 + ( 1 − 0 ) 2 ​ d = ( − 4 ) 2 + 1 ​ = 17 ​
b) Now we will write the equation of the circle:
( x − 5 ) 2 + y 2 = 17 ​ ​

Answered by Ryan2 | 2024-06-25

The equation of a circle with center (5, 0) that passes through the point (1, 1) can be derived by calculating the radius using the distance formula, resulting in a radius of 17 ​ . The final equation is ( x − 5 ) 2 + y 2 = 17 , which corresponds to option D. Therefore, the answer is D: ( x − 5 ) 2 + y 2 = 17 .
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Answered by Ryan2 | 2024-12-19