Question

Please help

Write the standard equation of a circle that passes through (−4, 0) with center (−1, −4).

(x + 4)2 + y2 = 25

(x + 1)2 + (y + 4)2 = 25

(x – 4)2 + y2 = 25

(x – 1)2 + (y – 4)2 = 25

Answer 1

The answer to your question is (x + 1)² + (y + 4)² = 25

Explanation:

Data

Point = (-4, 0)

Center = (-1, -4)

Process

1.- Calculate the length of the radius

dCP =
`\sqrt{(x2 - x1)^(2) + (y2 - y1)^(2)}`

-Substitution

dCP =
`\sqrt{(-1 + 4)^(2) + (-4 + 0)^(2)}`

-Simplification

dCP =
`\sqrt{3^(2)+ 4^(2)}`

dCP =
`√(9 + 16)`

dCP =
`√(25)`

dCP = 5

2.- Substitute the values in the equation of a circle

(x - h)² + (y - k)² = r²

(x + 1)² + (y + 4)² = 5²

(x + 1)² + (y + 4)² = 25