Question

write an equation for a circle with a diameter that has endpoints at (-4, -7) and (-2, -5). round to the nearest tenth if necessary.

Answer 1

The answer to your question is (x + 3)² + (y + 6)² = 2

Explanation:

Endpoints (-4, -7) and (-2, -5)

Process

1.- Find the length of the radius

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

d =
`\sqrt{(-2 + 4)^(2)+ (-5 + 7)^(2)  }`

d =
`\sqrt{2^(2) + 2^(2) }`

d =
`√(4 + 4)`

d =
`√(8)`

Radius =
`(√(8) )/(2)` =
`√(2)`

2.- Find the center

Xm =
`(-4 - 2)/(2) = (-6)/(2) = -3`

Ym =
`(-7 - 5)/(2) = (-12)/(2) = -6`

Center = (-3, -6)

3.- Write the equation

(x - h)² + (y - k)² = r²

(x + 3)² + (y + 6)² = (
`√(2)`)²

(x + 3)² + (y + 6)² = 2