Mathematics, 02.02.2020 15:54 ctuek5990

Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?

(x – 9)2 + (y + 4)2 = 25
(x + 4)2 + (y – 9)2 = 25
(x – 9)2 + (y + 4)2 = 100
(x + 4)2 + (y – 9)2 = 100

Answers: 1

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Answer from: Bloom247

(x + 4)² + (y - 9)² = 25

Further explanation

We will solve the problem by implementing the principle of the standard form of the circle equation.

The standard form of the circle equation, in other words the center-radius form, is $\boxed{\boxed{ \ (x - h)^2 + (y - k)^2 = r^2 \ }}$

Given:

Center of circle (-4, 9) Diameter or $\boxed{ \ 2 \times radius = 10 \ units \ } \rightarrow \boxed{ \ Radius \ r = 5 \units \ }$

The standard form

Again,

the center is at (h, k), in this case (-4, 9) the radius represent r = 5

$\boxed{ \ (x - (-4))^2 + (y - 9)^2 = 5^2 \ }$

So, we get the standard form of the circle equation.

$\boxed{\boxed{ \ (x + 4)^2 + (y - 9)^2 = 25 \ }}$

Let's explore this equation to be the general form of the circle equation.

The general form

Expand the equation, implement the square of the binomial pattern.

$\boxed{\boxed{ \ (a + b)^2 = a^2 = 2ab + b^2 \ }}$

$\boxed{ \ x^2 + 8x + 16 + y^2 - 18y + 81 = 25 \ }$

Rearrange the equation.

$\boxed{ \ x^2 + y^2 + 8x - 18y + 16 + 81 - 25 = 0 \ }$

We get the general form of the equation of the given circle.

$\boxed{\boxed{ \ x^2 + y^2 + 8x - 18y + 72 = 0 \ }}$

Learn more A similar problem Which equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)? Arc CD is ²/₃ of the circumference of a circle. What is the radian measure of the central angle?

Keywords: circle, standard form, equation, center, diameter, radius, squared binomial, center-radius form

Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units? (x – 9)2 +

Answer from: kanerobertrosss2213

The standard equation of circle with center at $\left( { - 4,9} \right)$ and diameter $10{\text{ units}}$ is ${\left( {x + 4} \right)^2} + {\left( {y - 9} \right)^2} = 25}$ .

Further explanation:

The standard equation of the circle with center $\left( {h,k} \right)$ and radius can be expressed as,

${\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}$ .

Given:

A circle with center at $\left( { - 4,9} \right)$ .

Diameter of the circle is $10{\text{ units}}$ .

Explanation:

The center is at $\left( { - 4,9} \right)$ .

Compare the general form $\left( {h,k} \right)$ of the center to the given center $\left( { - 4,9} \right)$ to obtain the value of and .

Therefore, the value of and are and respectively.

The radius of the circle is half as the diameter of the circle.

The relation between radius and diameter can be expressed as,

$r = \dfrac{d}{2}$

Substitute for in above equation to obtain the radius of the circle.

$\begin{gathered}r = \frac{{10}}{2} \\= 5 \\ \end{gathered}$

The radius of the circle is $5{\text{ units}}$ .

Substitute for , for and for to obtain the standard equation of the circle.

$\begin{gathered}{\left( {x - \left( { - 4} \right)} \right)^2} + {\left( {y - 9} \right)^2} = {\left( 5 \right)^2} \\{\left( {x + 4} \right)^2} + {\left( {y - 9} \right)^2} = 25 \\ \end{gathered}$

The standard equation of circle with center at $\left( { - 4,9} \right)$ and diameter $10{\text{ units}}$ is ${\left( {x + 4} \right)^2} + {\left( {y - 9} \right)^2} = 25$ .

$\fbox{\text{Option B}}$ is correct as the equation of circle is ${\left( {x + 4} \right)^2} + {\left( {y - 9} \right)^2} = 25$ .

Learn more:

1. Learn more about equation of circle

2. Learn more about domain of the function

3. Learn more about coplanar

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Circle

Keywords: Circle, standard form of the circle, equation of the circle, center, diameter of circle, radius of the circle, squared binomial, center-radius form, general equation of circle, tangent, area of circle, circumference of circle, arc of circle, chord.

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Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?

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