Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
(x - 4)² + y² = 100
(x - 4)² + y² = 10
x² + (y - 4)² = 10
x² + (y - 4)² = 100

Solution:

Given (-2, 8) is a point on the circle and (4, 0) is the origin of the circle

We know that the distance between centre and any point on the circle is called the radius of the circle

Radius = √{(y₂ - y₁)² + (x₂ - x₁)²}[Using the distance formula]

x₁ = -2, y₁ = 8, x₂ = 4, y₂ = 0

Radius = √{( 0 - 8)² + (4 - (-2))²}

Radius = √{(-8)² + (4 + 2)²}

Radius = √{64 + 36}

Radius = √100 

Radius = 10

We know that the equation of circle with circle (h, k) and radius r is given as (x - h)² +(y - k)² = r²

Here (h, k) = (4, 0)

(x - 4)² + (y - 0)² = 10²

(x - 4)² + y² = 100

x² - 8x + 16 + y² -100 = 0

x² + y² - 8x - 84 = 0

The equation of circle is x² + y² - 8x - 84 = 0

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Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?

Summary:

Equation x² + y² - 8x - 84 = 0 represents a circle that contains the point (-2, 8) and has a center at (4, 0).