Question

Select the correct answer from each drop-down menu. the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5). the center of the circle is at the point , and its radius is units. the equation of this circle in standard form is .

Answer 1

The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

h and k represent the coordinates at the center.

r is the radius of a circle.

The midpoint of the given points represents the center of this circle:

h = (4 + 4)/2 = 4

k = (5.5 + 10.5)/2 = 8

Next, we would determine the radius by using the distance formula for coordinates:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

r = √[(4 - 4)² + (10.5 - 5.5)²]

r = √[0² + 5²]

r = √25

r = 5 units.

Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Learn more about circle here: brainly.com/question/12823137

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