Equation of the Circle

mathxyz · 2024-02-27 04:21:34

The standard form of an equation of the circle of radius r and center at the origin (0, 0) is x^2 + y^2 = r^2.

The general form of an equation of a circle is given by
x^2 + y^2 + ax + by + c = 0.

The standard form of an equation of a circle with radius r and center
(h, k) is given by (x - h)^2 + (y - k)^2 = r^2.

Write the standard form and the general form of the equation of each circle of radius r and center (h, k) .

1. r = 3; (h, k) = (0, 0)

2. r = 7; (h, k) = (-5, -2)

Question 1

This circle is centered at the origin.

x^2 + y^2 = r^2

Let r = 3.

x^2 + y^2 = (3)^2

x^2 + y^2 = 9===>standard form

How do I write x^2 + y^2 = 9 in the general form
x^2 + y^2 + ax + by + c = 0?

Question 2

r = 7; (h, k) = (-5, -2)

This circle is not centered at the origin.

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

(x - (-5))^2 + (y - (-2))^2 = (7)^2

(x + 5)^2 + (y + 2))^2 = 49

(x + 5)(x + 5) + (y + 2)(y + 2) = 49

x^2 + 10x + 25 + y^2 + 4y + 4 = 49

I need to write it in the form x^2 + y^2 + ax + by + c = 0.

My answer is: x^2 + y^2 + 10x + 4y - 49 = 0.

You say?

Bob · 2024-02-27 06:17:18

Q1 Perfect.

Q2. Almost. Correct up to this line:

x^2 + 10x + 25 + y^2 + 4y + 4 = 49

You've brought the 49 across to the left hand side but forgotten there's already +25 and + 4 there.

Bob

KerimF · 2024-02-27 09:37:41

The general form of Q1 is:
x^2 + y^2 - 9 = 0

Last edited by KerimF (2024-02-27 09:38:32)

mathxyz · 2024-02-27 15:58:36

KerimF wrote:

The general form of Q1 is:
x^2 + y^2 - 9 = 0

Cool. Thanks.

mathxyz · 2024-02-27 16:03:25

Bob wrote:

Q1 Perfect.
Q2. Almost. Correct up to this line:
x^2 + 10x + 25 + y^2 + 4y + 4 = 49
You've brought the 49 across to the left hand side but forgotten there's already +25 and + 4 there.
Bob

In that case, the equation should be

x^2 + y^2 + 10x + 4y - 20 = 0

Yes?

KerimF · 2024-02-27 19:34:51

FelizNYC wrote:

In that case, the equation should be
x^2 + y^2 + 10x + 4y - 20 = 0
Yes?

Yes.

mathxyz · 2024-02-28 03:51:19

KerimF wrote:

FelizNYC wrote:
In that case, the equation should be
x^2 + y^2 + 10x + 4y - 20 = 0
Yes?
Yes.

Perfect. I will post similar questions when time allows.

KerimF · 2024-03-01 11:36:16

FelizNYC wrote:

The standard form of an equation of a circle with radius r and center (h, k) is given by:
(x - h)^2 + (y - k)^2 = r^2.

mathxyz · 2024-03-02 19:00:36

KerimF wrote:

FelizNYC wrote:
The standard form of an equation of a circle with radius r and center (h, k) is given by:
(x - h)^2 + (y - k)^2 = r^2.

What is your comment here?

KerimF · 2024-03-03 05:04:42

FelizNYC wrote:

KerimF wrote:
FelizNYC wrote:
The standard form of an equation of a circle with radius r and center (h, k) is given by:
(x - h)^2 + (y - k)^2 = r^2.
What is your comment here?

Sorry, it was just a reminder since, while you know it well, you used to miss applying it in your previous first solutions.

mathxyz · 2024-03-03 18:20:08

KerimF wrote:

FelizNYC wrote:
What is your comment here?
Sorry, it was just a reminder since, while you know it well, you used to miss applying it in your previous first solutions.

Miss applying???

KerimF · 2024-03-03 22:39:05

Sorry again, do I need searching the posts of your 'first' wrong solutions (not the ones later) when you used to apply x^2 + y^2 = r^2 instead of (x - h)^2 + (y - k)^2 = r^2?

mathxyz · 2024-03-04 01:55:42

KerimF wrote:

Sorry again, do I need searching the posts of your 'first' wrong solutions (not the ones later) when you used to apply x^2 + y^2 = r^2 instead of (x - h)^2 + (y - k)^2 = r^2?

Sometimes I rush through each problem leading to confusion.
Why rush? Lack of time is the reason. I work 40 overnight hours. I travel 90 minutes to and from work on 3 trains. All my time is dedicated to the job and crazy commuting.

KerimF · 2024-03-04 03:45:15

FelizNYC wrote:

KerimF wrote:
Sorry again, do I need searching the posts of your 'first' wrong solutions (not the ones later) when you used to apply x^2 + y^2 = r^2 instead of (x - h)^2 + (y - k)^2 = r^2?
Sometimes I rush through each problem leading to confusion.
Why rush? Lack of time is the reason. I work 40 overnight hours. I travel 90 minutes to and from work on 3 trains. All my time is dedicated to the job and crazy commuting.

This is good news. You don't have time to feel bored

mathxyz · 2024-03-04 22:14:43

KerimF wrote:

FelizNYC wrote:
KerimF wrote:
Sorry again, do I need searching the posts of your 'first' wrong solutions (not the ones later) when you used to apply x^2 + y^2 = r^2 instead of (x - h)^2 + (y - k)^2 = r^2?
Sometimes I rush through each problem leading to confusion.
Why rush? Lack of time is the reason. I work 40 overnight hours. I travel 90 minutes to and from work on 3 trains. All my time is dedicated to the job and crazy commuting.
This is good news. You don't have time to feel bored

No brother, rushing leads to senseless errors. Rushing leads to anxiety issues.

Math Is Fun Forum

#1 2024-02-27 04:21:34

Equation of the Circle

#2 2024-02-27 06:17:18

Re: Equation of the Circle

#3 2024-02-27 09:37:41

Re: Equation of the Circle

#4 2024-02-27 15:58:36

Re: Equation of the Circle

#5 2024-02-27 16:03:25

Re: Equation of the Circle

#6 2024-02-27 19:34:51

Re: Equation of the Circle

#7 2024-02-28 03:51:19

Re: Equation of the Circle

#8 2024-03-01 11:36:16

Re: Equation of the Circle

#9 2024-03-02 19:00:36

Re: Equation of the Circle

#10 2024-03-03 05:04:42

Re: Equation of the Circle

#11 2024-03-03 18:20:08

Re: Equation of the Circle

#12 2024-03-03 22:39:05

Re: Equation of the Circle

#13 2024-03-04 01:55:42

Re: Equation of the Circle

#14 2024-03-04 03:45:15

Re: Equation of the Circle

#15 2024-03-04 22:14:43

Re: Equation of the Circle

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