Standard Form of the Equation of a Circle

[nycmathguy]

Homework Statement

Write standard form of equation of a circle.

Relevant Equations

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

Chapter 1, Section 1.2

Write the standard form of the equation of the circle with the given characteristics.

72. Center: (−2, −6); Solution point: (1, −10)

Solution:

given: Center: (−2, −6); => h=-2, k=-6

=> then (x - (-2))^2 + (y - (-6))^2 = r^2

(x +2)^2 + (y +6)^2 = r^2...

I then use the given solution point to calculate r^2.

(1 +2)^2 + (-10+6)^2 = r^2
9 + 16 = r^2
25 = r^2

Equation is:

(x +2)^2 + (y +6)^2 = 25

You say?

 

[.Scott]

Looks good to me.

 

[nycmathguy]

Looks good to me.

Thanks...

 

[Mark44]

Homework Statement:: Write standard form of equation of a circle.
Relevant Equations:: (x - h)^2 + (y - k)^2 = r^2

Good. These are what I was trying to get you to include in your other threads.

72. Center: (−2, −6); Solution point: (1, −10)
Solution:
given: Center: (−2, −6); => h=-2, k=-6

Equation is:
(x +2)^2 + (y +6)^2 = 25

You say?

Instead of writing "You say?" all you need to do is to check your answer. Is the center at (-2, -6)? Obviously it is. Does the point (1, -10) lie on the circle? If so, then the equation $(1 + 2)^2 + (-10 + 6)^2 = 25$ will be a true statement.

An essential part of doing problems like this is to check your work.

 

[PeroK]

Another idea is to try to think of an independent way of checking this. Geometrically a circle has a centre and a radius ($r$). You could plot those two points $(-2, -6)$ and $(1, -10)$ and check that the distance between them is $r = 5$.

That's not only an independent check of your solution, but reinforces the connection between equations and geometric shapes.

 

[symbolipoint]

Homework Statement:: Write standard form of equation of a circle.
Relevant Equations:: (x - h)^2 + (y - k)^2 = r^2

Chapter 1, Section 1.2

Write the standard form of the equation of the circle with the given characteristics.

72. Center: (−2, −6); Solution point: (1, −10)

Solution:

given: Center: (−2, −6); => h=-2, k=-6

=> then (x - (-2))^2 + (y - (-6))^2 = r^2

(x +2)^2 + (y +6)^2 = r^2...

I then use the given solution point to calculate r^2.

(1 +2)^2 + (-10+6)^2 = r^2
9 + 16 = r^2
25 = r^2

Equation is:

(x +2)^2 + (y +6)^2 = 25

You say?

I cannot recall exactly which course you are studying, but this question is typical of Intermediate Algebra. You can and at times should, make use of the Distance Formula definitions for the Conic Sections. That can give you your answer to your question here for

"Write the standard form of the equation of the circle with the given characteristics.

72. Center: (−2, −6); Solution point: (1, −10)".Naturally, if you already have and understand the standard formula for circle, you can use it directly.SMALL MISREAD: The "72" would seem to be an exercise identifier number, and not part of the problem's description. Making use of the generic standard formula of equation of a circle would be a good choice for this exercise.

 

[nycmathguy]

I cannot recall exactly which course you are studying, but this question is typical of Intermediate Algebra. You can and at times should, make use of the Distance Formula definitions for the Conic Sections. That can give you your answer to your question here for

"Write the standard form of the equation of the circle with the given characteristics.

72. Center: (−2, −6); Solution point: (1, −10)".Naturally, if you already have and understand the standard formula for circle, you can use it directly.SMALL MISREAD: The "72" would seem to be an exercise identifier number, and not part of the problem's description. Making use of the generic standard formula of equation of a circle would be a good choice for this exercise.

I am doing a self-study of precalculus. As you know, precalculus covers a little bit of everything.

 

[symbolipoint]

I am doing a self-study of precalculus. As you know, precalculus covers a little bit of everything.

Pre-Calculus is a very tough course for some people. More precisely it includes all of "Algebra 1" and "Algebra 2", and goes further, including more on sequences & series, and polynomial functions, and of degree greater than just 2.

Important advice for you is:

• Be sure you review an Algebra 1 course, thoroughly.
• Be sure you study or review an Algebra 2 course, thoroughly. Be sure you are officially assessed to have earned a B or better.
• One could review or study those two on his own but one really should attend an actual institution, such as a community college.
• One can not afford to be weak at the Intermediate Algebra level when beginning to study Pre-Calculus, since in many ways Pre-Calculus is a continuation from Intermediate Algebra.

More can be said but I will leave just those advisories for now.

 

[nycmathguy]

Pre-Calculus is a very tough course for some people. More precisely it includes all of "Algebra 1" and "Algebra 2", and goes further, including more on sequences & series, and polynomial functions, and of degree greater than just 2.

Important advice for you is:

• Be sure you review an Algebra 1 course, thoroughly.
• Be sure you study or review an Algebra 2 course, thoroughly. Be sure you are officially assessed to have earned a B or better.
• One could review or study those two on his own but one really should attend an actual institution, such as a community college.
• One can not afford to be weak at the Intermediate Algebra level when beginning to study Pre-Calculus, since in many ways Pre-Calculus is a continuation from Intermediate Algebra.

More can be said but I will leave just those advisories for now.

1. I am not a classroom student.

2. I am 56 years old.

3. I work 40 overnight hours during the week, which means that sleeping during the day is a must. I only have Saturday and Sunday to dedicate a few hours to any study.

4. Precalculus is a review for me. I took this course at Lehman College in the Spring 1993 semester. I got an A minus. Not bad for someone who did not major in mathematics.

5. The questions you see here come from a precalculus textbook by Ron Larson Edition 10E.
I understand, however, why some are asking themselves: WHAT IS THIS nycmathguy actually learning?

 

[symbolipoint]

1. I am not a classroom student.

2. I am 56 years old.

3. I work 40 overnight hours during the week, which means that sleeping during the day is a must. I only have Saturday and Sunday to dedicate a few hours to any study.

4. Precalculus is a review for me. I took this course at Lehman College in the Spring 1993 semester. I got an A minus. Not bad for someone who did not major in mathematics.

5. The questions you see here come from a precalculus textbook by Ron Larson Edition 10E.
I understand, however, why some are asking themselves: WHAT IS THIS nycmathguy actually learning?

I still believe that for even reviewing Pre-Calculus any significant number of years after earning the credit, you should thoroughly review Intermediate Algebra, and restudy it with the intent of perfection, or near to perfection. Official credit may last you a lifetime but the meaning of the grade you earned spoils very fast unless you maintain it or re-build it.

The tough part of your situation is that you only have two days in the week when you can study. A PERSON MUST STUDY MATHEMATICS COURSEWORK ALMOST EVERY DAY if he wants to be competent in it.

 

[nycmathguy]

I still believe that for even reviewing Pre-Calculus any significant number of years after earning the credit, you should thoroughly review Intermediate Algebra, and restudy it with the intent of perfection, or near to perfection. Official credit may last you a lifetime but the meaning of the grade you earned spoils very fast unless you maintain it or re-build it.

The tough part of your situation is that you only have two days in the week when you can study. A PERSON MUST STUDY MATHEMATICS COURSEWORK ALMOST EVERY DAY if he wants to be competent in it.

Yes, I know that DAILY STUDY TIME is the key to success. However, my job, my money, paying my bills, eating, etc takes preference over math books and questions. My health is also more important than mathematics. Without health, I cannot study. Without health, I die. Without health, my mind becomes a vegetable.

 

[Vanadium 50]

Another idea is to try to think of an independent way of checking this. Geometrically a circle has a centre and a radius. You could plot those two points and and check that the distance between them is .

Also, you know the center and one point. Therefore you know a second point. Is it on the circle too?

 

[DaveE]

I work 40 overnight hours during the week, which means that sleeping during the day is a must. I only have Saturday and Sunday to dedicate a few hours to any study.

A few a hours a week is OK, but you'll need to focus and use that time well. Of course, you won't learn as fast as people that study more (duh!). If you really need this for your future work, then that's not enough time, but it's fine if it's for entertainment or personal growth. Recognize that you will have to pace yourself and limit your expectations accordingly (you will never learn the Maths of General Relativity at that rate). This is where you should follow the advice of others that know the material and the "normal" curriculum path. Also recognize that most everyone here studied much harder than that and does this as part of their profession. We are not that familiar with your situation, but we do know what you should study next.

Precalculus is a review for me. I took this course at Lehman College in the Spring 1993 semester. I got an A minus. Not bad for someone who did not major in mathematics.

Congratulations on your grade from about 30 years ago. Trust me, we don't think your stupid. However, Pre-calculus is NEVER really targeted at math majors. In my experience, most math majors, as well as all STEM fields, start college with a good understanding of basic calculus. Those that don't learn it immediately.

Don't apologize for what you don't know yet. We all don't know stuff. But also be realistic about where you are and where you can go given the limitations on your time.

 

[nycmathguy]

A few a hours a week is OK, but you'll need to focus and use that time well. Of course, you won't learn as fast as people that study more (duh!). If you really need this for your future work, then that's not enough time, but it's fine if it's for entertainment or personal growth. Recognize that you will have to pace yourself and limit your expectations accordingly (you will never learn the Maths of General Relativity at that rate). This is where you should follow the advice of others that know the material and the "normal" curriculum path. Also recognize that most everyone here studied much harder than that and does this as part of their profession. We are not that familiar with your situation, but we do know what you should study next.Congratulations on your grade from about 30 years ago. Trust me, we don't think your stupid. However, Pre-calculus is NEVER really targeted at math majors. In my experience, most math majors, as well as all STEM fields, start college with a good understanding of basic calculus. Those that don't learn it immediately.

Don't apologize for what you don't know yet. We all don't know stuff. But also be realistic about where you are and where you can go given the limitations on your time.

I will not go back to prealgebra material. Forget algebra 1 and 2. I plan to review geometry in the future. Precalculus covers enough trigonometry for me to review once I get to that chapter.

 

[symbolipoint]

Some picking through these parts a little bit:

I will not go back to prealgebra material.

Good. You should probably not need it.

Forget algebra 1 and 2.

NO! Remember them and become highly competent in those. YOU NEED THOSE LEVELS IN COLLEGE ALGEBRA/PRECALCULUS.
For this part here, Geometry review any time after mastering Algebra 1, but keep it mastered, or build it back up.

I plan to review geometry in the future.

 

[nycmathguy]

Some picking through these parts a little bit:Good. You should probably not need it.NO! Remember them and become highly competent in those. YOU NEED THOSE LEVELS IN COLLEGE ALGEBRA/PRECALCULUS.
For this part here, Geometry review any time after mastering Algebra 1, but keep it mastered, or build it back up.

Revisiting math courses learned long ago in my youth one day at a time.