Question

I need an answer asap. I really would like some help with this

Answer 1

(x + 4)² + (y + 1)² = 4

Explanation:

From the graph attached,

Extreme ends of the diameter of the circle,

(-4, 1) and (-4, -3)

Center of the circle = Midpoint of the diameter

Center =
`((x_1+x_2)/(2), (y_1+y_2)/(2))`

=
`((-4-4)/(2),(1-3)/(2))`

= (-4, -1)

Radius of the circle = Distance between the center and extreme end

= 2 units

Since standard equation of the circle is,

(x - h)² + (y - k)² = r²

where (h, k) is the center and 'r' is the radius of the circle

By substituting the values in the standard equation,

(x + 4)² + (y + 1)² = 2²

(x + 4)² + (y + 1)² = 4