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Irina18 [472]
3 years ago
6

Select the correct answer from each drop-down menu.

Mathematics
1 answer:
serious [3.7K]3 years ago
6 0

Answer:

Center: (4,8)

Radius: 2.5

Equation: (x-4)^2+(y-8)^2=6.25

Step-by-step explanation:

It was given that; the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

Note that the longest chord is the diameter;

The midpoint of the ends of the diameter gives us the center;

Use the midpoint formula;

(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )

The center is at; (\frac{4+4)}{2} ,\frac{5.5+10.5}{2}=(4,8)

To find the radius, use the distance formula to find the distance from the center to one of the endpoints.

The distance formula is;

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

r=\sqrt{(4-4)^2+(10.5-8)^2}

r=\sqrt{0^2+(2.5)^2}

r=\sqrt{0^2+(2.5)^2}=2.5

The equation of the circle in standard form is given by;

(x-h)^2+(y-k)^2=r^2

We substitute the center and the radius into the formula to get;

(x-4)^2+(y-8)^2=2.5^2

(x-4)^2+(y-8)^2=6.25

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