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Circle Equations

Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle.

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This is level 1: equations of circles.

1) Circle Equations
Which of the following is the equation of the circle above?

a) \(x^2 + y^2 = 16\)
b) \(x^2 + y^2 = 4\)
c) \(x^2 + y^2 = 8\)
Correct Wrong
2) The equation of a circle is \(x^2 + y^2 = 16\). What is the radius of the circle? Correct Wrong
3) The equation of a circle is \(x^2 + y^2 = 56.25\). What is the radius of the circle? Correct Wrong
4) Which of the following is the equation of a circle with centre at the origin and a radius of 13 units?
a) \(x^2 + y^2 = 169\)
b) \(x^2 + y^2 = 13\)
c) \(x^2 + y^2 = 26\)
Correct Wrong
5) The equation of a circle is \(5x^2 + 5y^2 = 320\). What is the radius of the circle? Correct Wrong
6) The equation of a circle is \(6x^2 + 6y^2 = 54\). What is the radius of the circle? Correct Wrong
7) Which of the following is the equation of a circle with centre at the origin and a radius of 8 units?
a) \(2x^2 + 2y^2 = 64\)
b) \(x^2 + y^2 = 8\)
c) \(2x^2 + 2y^2 = 128\)
Correct Wrong
8) Which of the following is the equation of a circle with centre at the origin which passes through the point (3,4)?
a) \(12x^2 + 12y^2 = 25\)
b) \(6x^2 + 6y^2 = 150\)
c) \(18x^2 + 18y^2 = 25\)
Correct Wrong
9) Which of the following is the equation of a circle with centre at the origin and a radius of \(2 \sqrt{2}\) units?
a) \(2x^2 + 2y^2 = 4\)
b) \(2x^2 + 2y^2 = 8\)
c) \(x^2 + y^2 = 8\)
Correct Wrong
10) The equation of a circle is given as \(y^2 = (6+x)(6-x)\). What is the radius of the circle? Correct Wrong
Check

This is Circle Equations level 1. You can also try:
Level 2

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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Level 1 - Equations of circles

Level 2 - Equations of tangents to circles

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

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Example

The video above is from the wonderful Corbettmaths.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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