CIRCLE | TRANSFORMING STANDARD FORM TO GENERAL FORM | PROF D

Precalculus
Equation of Circle
Transforming standard form to general form
Graphing circles requires two things: the coordinates of the center point, and the radius of a circle. A circle is the set of all points the same distance from a given point, the center of the circle. A radius,
r, is the distance from that center point to the circle itself.
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Thanks Prof D, exam namin ngayon sa Pre-Cal and this helped a lot. ❤

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[@nicocesario.6185]

CESARIO, NICO TAM TAM A.
STEM1202
Thankyou for this, Prof.D!
This video is really informative. I've learned that the standard form of the equation of a circle is ...
(x -h)² +(y -k)² = r² . . . . . .circle centered at (h, k) with radius r
The general form of the equation of a circle will be ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0 . . . . . A = C for a circle
The former is converted to the latter by eliminating parentheses, subtracting r² and collecting terms.
x² +y² -2hx -2ky +(h² +k² -r²) = 0
This shows you that ...
A = C = 1
B = 0
D = -2h
E = -2k
F = h² +k² -r²
In general form, we like to have the coefficients be mutually prime integers and the leading coefficient be positive. That is not always possible, depending on the circle being represented

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[@princessannelcedano537]

YOUR STUDENT FROM GAS1214
I JUST FINISHED WATCHING AND I HAVE LEARNED THAT THERE ARE TWO METHODS TO GET THE GENERAL FORM OF THE CIRCLE. FOR ME IT WAS EASY TO USE THE METHOD 1 BECAUSE I JUST NEED TO GET THE STANDARD FORM THEN I JUST NEED TO EXPAND THE SQUARE OF BINOMIALS AND AFTER THAT I NEED TO REARRANGE THE EQUATIONS AND COMBINING LIGHT TERMS AND THATS THE GENERAL FORM OF THE CIRCLE. I REALLY ENJOYED LEARNING THANYOUSOMUCH

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Thankyou po sirrr, finished watching from 11-stem of CHS, i kinda struggle understanding the method 2 pero sobrang galing nyopo, I was having a relly hard time when our Teacher's the one who's explaining it pero nagets kona nung kayo, so I'm veryy veryy thankful that I watched thiss!!❤

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[@adriennejoypagaling5697]

Good morning po Prof, ask lang po about dun sa method 2. Yung d = - 2h , e = - 2k, f= h2 + k2 - r2 .
Pwede po ba yan sa kahit anong equation? I mean, ayan po ba ay formula to get po the general form?

[@ProfD]

Sa lahat ng conics pwede yan, pero usually sa circle na lang sya ginagamit

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