Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Equation of the Circle...Again

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) .

r = 3; (h, k) = (1, -2)

Let me see.

This circle is not centered at the origin.

Plug r = 3, h = 1, and k = -2 into

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

(x - 1)^2 + (y - (-2))^2 = 3^2

(x - 1)^2 + (y + 2)^2 = 9....This is the standard form not centered at the origin.

Next, write the general form of the equation of the circle.

(x - 1)^2 + (y + 2)^2 = 9

(x - 1)(x - 1) + (y + 2)(y + 2) - 9 = 0

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0

x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

x^2 + y^2 - 2x + 4y - 3 = 0

You say?

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 165

Re: Equation of the Circle...Again

(x - 1)^2 + (y + 2)^2 = 9
...
x^2 + y^2 - 2x + 4y - 3 = 0

(x - 1)^2 + (y + 2)^2 = 9

Let us assume x=1:
(1 - 1)^2 + (y + 2)^2 = 9
(y + 2)^2 = 9
y + 2 = 3
y = 3 - 2
y = 1

Now,
x^2 + y^2 - 2x + 4y - 3 = 0

Let us verify if this final form is also satisfied for x=1 and y=1
1^2 + 1^2 - 2*1 + 4*1 - 3 = 0
1 + 1 - 2 + 4 - 3 = 1 ≠ 0

I am afraid that you did a typo somewhere.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Equation of the Circle...Again

(x - 1)^2 + (y + 2)^2 = 9
...
x^2 + y^2 - 2x + 4y - 3 = 0

(x - 1)^2 + (y + 2)^2 = 9

Let us assume x=1:
(1 - 1)^2 + (y + 2)^2 = 9
(y + 2)^2 = 9
y + 2 = 3
y = 3 - 2
y = 1

Now,
x^2 + y^2 - 2x + 4y - 3 = 0

Let us verify if this final form is also satisfied for x=1 and y=1
1^2 + 1^2 - 2*1 + 4*1 - 3 = 0
1 + 1 - 2 + 4 - 3 = 1 ≠ 0

I am afraid that you did a typo somewhere.

Can you show me where the error was made?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Equation of the Circle...Again

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0

x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

The plus 4 on the correct line has become plus 5 on the next line.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 165

Re: Equation of the Circle...Again

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0
x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0
to
x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

It is actually:
x^2 + y^2 - 2x + 4y + 1 + 4 - 9 = 0

Your typo was 5 instead of 4.
I recall how, me too, I did this type of mistake in some math exams (when I was a student many decades ago). I even failed in one of them because of a silly typo I did.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Equation of the Circle...Again

hi KerimF

Didn't spot you were on line too.  Looks like we both saw the same thing

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 165

Re: Equation of the Circle...Again

hi KerimF
Didn't spot you were on line too.  Looks like we both saw the same thing
Bob

Off topic, after I realized, at school, that I can't avoid doing typo mistakes (not only in math), I used after finishing an exam (or the like) to revise what I did but as if I were a bad rival of Kerim who insisted to show him (Kerim) the many mistakes he did. By doing this seriously, it was possible for me to get the highest grade in most exams.

Kerim

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Equation of the Circle...Again

My first attempt at every post is usually full of typos.  After I've read it through and corrected a few times I think I've got an error free post.  Let me know if you discover this statement is false.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 165

Re: Equation of the Circle...Again

My first attempt at every post is usually full of typos.  After I've read it through and corrected a few times I think I've got an error free post.  Let me know if you discover this statement is false.

Bob

Same is here. I never write something new without editing it several times.
So, at work, I see myself having a good luck if I can end up writing an error free code (for MCU) after correcting 50 bugs, not 500's, if not more, which happened sometimes

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Equation of the Circle...Again

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0
x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0
to
x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

It is actually:
x^2 + y^2 - 2x + 4y + 1 + 4 - 9 = 0

Your typo was 5 instead of 4.
I recall how, me too, I did this type of mistake in some math exams (when I was a student many decades ago). I even failed in one of them because of a silly typo I did.

I got it. Thanks. It was simply a typo.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Equation of the Circle...Again

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0

x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

The plus 4 on the correct line has become plus 5 on the next line.

Bob

Thank you. Someone else pointed out my typo. Rest assure that this is simply a self-study of math learned back in the 80s and 90s. What else is a middle-aged lonely guy to do?

TWO LOVES

1. MATHEMATICS

2. CLASSICAL GUITAR HYMNS

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Equation of the Circle...Again

TWO LOVES

1. MATHEMATICS

2. CLASSICAL GUITAR HYMNS

Hi, solo_guitar!

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Equation of the Circle...Again

TWO LOVES

1. MATHEMATICS

2. CLASSICAL GUITAR HYMNS

Hi, solo_guitar!

What? Who cares? Stick to question at hand.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Equation of the Circle...Again

Hi, solo_guitar!

What? Who cares? Stick to question at hand.

i saw you posting again abt playing guitar so I said hi
Sry i made you mad again

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Equation of the Circle...Again

Hi, solo_guitar!

What? Who cares? Stick to question at hand.

i saw you posting again abt playing guitar so I said hi
Sry i made you mad again

I am not mad. It takes a lot to get me mad. We can discuss the guitar in another forum.