Determinar el centro y radio de una circunferencia completando cuadrados

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Luis Hernandez

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6 years, 2 months ago

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Ricardo Monge was given access to the Determinar el centro y radio de una circunferencia completando cuadrados 4 years, 3 months ago

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Luis Hernandez 6 years, 2 months ago

Gave some feedback: Ready to use

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Luis Hernandez 6 years, 2 months ago

Created this as a copy of Graphing: circles - completing the square.

Name	Status	Author	Last Modified
Solving a quadratic by using the quadratic formula - integer coefficients	Ready to use	Ben Brawn	21/03/2025 04:36
Solving a quadratic by completing the square	Ready to use	Ben Brawn	05/02/2025 01:18
Graphing: circles - completing the square	Ready to use	Ben Brawn	20/03/2025 01:54
Week 6: Quadratic formula	Ready to use	Ashley Cusack	04/12/2017 13:26
Solving a quadratic ( formula)	Ready to use	heike hoffmann	14/11/2018 22:45
Determinar el centro y radio de una circunferencia completando cuadrados	Ready to use	Luis Hernandez	28/03/2021 16:08
Terry's copy of Solving a quadratic by using the quadratic formula	draft	Terry Young	03/04/2019 17:19
Terry's copy of Solving a quadratic by completing the square	draft	Terry Young	03/04/2019 17:36
Solving a quadratic by using the quadratic formula	draft	Xiaodan Leng	10/07/2019 22:13
Musa's copy of 3 Solving a quadratic by using the quadratic formula	draft	Musa Mammadov	27/06/2023 01:26

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Question statement

Considere la ecuación general de la circunferencia

$\simplify[basic,fractionNumbers]{{scoeff}x^2+{lcoeff}x+{scoeff}y^2+{m}y+{k}={c}}.$

Reducir la ecuación a la forma estandar y responde:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
b	integer	3
c	integer	2
dd	integer	4
d	integer	4
scoeff	integer	12
lcoeff	integer	22
ccoeff	integer	8
disc	number	100
lengthdet	number	10
div	rational	11/6
argtop	number	100
argbot	number	576
sqrtargtop	number	10
sqrtargbot	number	24
m	integer	3
k	number	10.1875
xcentre	rational	-11/12
ycentre	rational	-1/8
radius	decimal	dec("4.166666666666666666666666666666666666667e-1")
switch	integer	0

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..5)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

d
k
lcoeff
lengthdet
m
radius
scoeff

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
1. Step Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

La ecuación representa una circunferencia círculo con radio. Gap 0. y centro en el punto $\large($ Gap 1., Gap 2. $\large)$ .

Advice

Recuerde que
$(x+a)^2=x^2+2ax+a^2$
es un cuadrado perfecto. Ahora, note que si $b=2a$ esta ecuación llegaría a ser
$\left(x+\frac{b}{2}\right)^2=x^2+bx+\left(\frac{b}{2}\right)^2$ .
Completamos los cuadrados:

$\simplify[basic,basic,fractionNumbers]{{scoeff}x^2+{lcoeff}x+{scoeff}y^2+{m}y+{k}}$	$=$	$\var{c}$
$\simplify[basic,basic,fractionNumbers]{{scoeff}x^2+{lcoeff}x+{scoeff}y^2+{m}y}$	$=$	$\simplify[basic,fractionNumbers]{{c-k}}$	(obtener todas las constantes en el lado derecho)
$\simplify[basic,fractionNumbers]{x^2+{lcoeff}/{scoeff}x}+\simplify[basic,fractionNumbers]{y^2+{m}/{scoeff}y}$	$=$	$\simplify[basic,fractionNumbers]{{(c-k)/scoeff}}$	(Divide cada término por el coeficiente de $x^2$ )
$\simplify[basic,fractionNumbers]{x^2+{lcoeff/scoeff}x+{lcoeff^2/(4scoeff^2)}}+\simplify[basic,fractionNumbers]{y^2+{m/scoeff}y+{m^2/(4scoeff^2)}}$	$=$	$\simplify[basic,fractionNumbers]{{(c-k)/scoeff}}+\simplify{{lcoeff^2}/{4scoeff^2}}+\simplify{{m^2}/{4scoeff^2}}$	(para $x$ y $y$ : agregue a ambos lados el cuadrado de la mitad del coeficiente)
$(\simplify[basic,fractionNumbers]{x+{-xcentre}})^2+(\simplify[basic,fractionNumbers]{y+{-ycentre}})^2$	$=$	$\simplify[basic,fractionNumbers]{{radius^2}}$	(reescribe el lado izquierdo como dos cuadrados perfectos)
$(\simplify[basic,fractionNumbers]{x+{-xcentre}})^2+(\simplify[basic,fractionNumbers]{y+{-ycentre}})^2$	$=$	$\left(\simplify[basic,fractionNumbers]{{radius}}\right)^2$

De esta ecuación podemos concluir que la ecuación es de un círculo de radio $\simplify[basic,fractionNumbers]{{radius}}$ with centre $\left(\simplify[basic,fractionNumbers]{{xcentre}},\simplify[basic,fractionNumbers]{{ycentre}}\right)$ .

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
Number entry
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Number entry
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Determinar el centro y radio de una circunferencia completando cuadrados

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Ricardo Monge was given access to the Determinar el centro y radio de una circunferencia completando cuadrados 4 years, 3 months ago

Luis Hernandez 6 years, 2 months ago

Luis Hernandez 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Determinar el centro y radio de una circunferencia completando cuadrados

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ricardo Monge was given access to the Determinar el centro y radio de una circunferencia completando cuadrados 4 years, 3 months ago

Luis Hernandez 6 years, 2 months ago

Luis Hernandez 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`