Centre and radius of a circle

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

Feedback

From users who are not members of Content created by Newcastle University :

Rob Beckett

said

Ready to use

6 years, 9 months ago

History

○

Rob Beckett 6 years, 9 months ago

Gave some feedback: Ready to use

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

There is only one version of this question that you have access to.

There are 13 other versions that do you not have access to.

Question statement

Find the centre and radius of the circle with equation

$\simplify[std]{x^2+y^2 -{2*a}x -{2*b}y+{a^2+b^2-r^2}}=0.$

Input the coordinates of the centre and the radius as integers.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
r	integer	3
b	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-5..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:

Statement
Advice
"Unnamed part" → "Gap 0." - Correct answer

Parts

Gap-fill

Gap-fill

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

The centre is (Gap 0.,Gap 1.). The radius is Gap 2..

Advice

Complete the square for each of $x$ and $y$ : $~~~\simplify[std]{x^2-{2*a}x =(x-{a})^2-{a^2}}$ and $\simplify[std]{y^2 -{2*b}y=(y-{b})^2-{b^2}}$ .

Therefore $\simplify[std]{x^2+y^2 -{2*a}x -{2*b}y+{a^2+b^2-r^2}=(x-{a})^2-{a^2}+(y-{b})^2-{b^2}+{a^2+b^2-r^2}}$

and the equation of the circle becomes $\simplify[std]{(x-{a})^2+(y-{b})^2={r^2}}$ .

It follows that the centre is $(\var{a}, \var{b})$ and the radius is $\var{r}$ .

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

FC review of line, circle and trigonometry by Deirdre Casey in Deirdre's workspace.
David's copy of Foundation mathematics by David Rickard in David's workspace.
Foundation mathematics by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Math III Spring 2016 Review 2 by Ethan Smith in Ethan's workspace.
P2 - Coordinate Geometry by Rob Beckett in Rob's workspace.
NUMBAS - More Circles by Katy Dobson in Katy's workspace.
Foundation mathematics quiz by Simon Thomas in Foundation mathematics.
Maria's copy of Foundation mathematics by Maria Aneiros in Maria's workspace.
Ann's copy of Foundation mathematics by Ann Smith in Foundation Maths.
Week 4 - Equation of a circle by John Harvey in Swansea MA-004.
Workshop testing by Elizabeth Petrie in Elizabeth's workspace.
Ben's copy of Foundation mathematics by Ben Sathuluri in Ben's workspace.
Foundation of Maths by Chris Templet in Chris's workspace.
Robert's copy of Foundation mathematics by Robert Barham in Robert's workspace.
claire's copy of Foundation mathematics by claire lines in claire's workspace.
Week 17 e-quiz by Ruth Douglas in Ruth's workspace.
Subject Knowledge Homework 1 by Ciaran Cassidy in A Level Subject Knowledge Homework.
ME0006 Wk 1 Test 3 by claire lines in claire's workspace.
Testing package by Niall Barr in Niall's workspace.
Engineering First Year Skills Audit by S Russell in Engineering Maths booster.
BE1607 Wk 3 general Test by claire lines in claire's workspace.
Deborahs Test 2 by Deborah Bruce in Deborah's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Rob Beckett 6 years, 9 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Centre and radius of a circle

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Rob Beckett 6 years, 9 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`