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What is the standard form of the equation of a circle whose diameter is 20 units and whose center is (−1,7)?

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What is the standard form of the equation of a circle whose diameter is 20 units and whose center is 17 Drag an expression or value to the boxes to correctly co class=

Respuesta :

akposevictor

Answer:

[tex] (x + 1)^2 + (y - 7)^2 = 100 [/tex]

Step-by-sep explanation:

Given:

Diameter of circle = 20 units

Center of circle = (-1, 7)

Standard form of the equation of a circle is expressed in the center-radius form as:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex],

Where,

h = -1

k = 7

r = ½ of diameter = ½(20) = 10 units

Plug in the values into the equation

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

[tex] (x - (-1))^2 + (y - 7)^2 = 10^2 [/tex]

[tex] (x + 1)^2 + (y - 7)^2 = 100 [/tex]

MrRoyal

The equation of the circle is [tex]\mathbf{(x +1)^2 + (y -7)^2 =100}[/tex]

The standard form of the equation of a circle is:

[tex]\mathbf{(x -a)^2 + (y -b)^2 =r^2}[/tex]

From the question, we have:

[tex]\mathbf{(a,b) = (-1,7)}[/tex]

[tex]\mathbf{r = \frac{1}{2} \times 20 = 10}[/tex]

So, the equation becomes

[tex]\mathbf{(x -a)^2 + (y -b)^2 =r^2}[/tex]

Substitute values for (a), (b) and (r)

[tex]\mathbf{(x +1)^2 + (y -7)^2 =10^2}[/tex]

Express 10^2 as 100

[tex]\mathbf{(x +1)^2 + (y -7)^2 =100}[/tex]

Hence, the equation of the circle is [tex]\mathbf{(x +1)^2 + (y -7)^2 =100}[/tex]

Read more about equations of circles at:

https://brainly.com/question/23988015

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