Circle Equations

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

Level 1Level 2Exam-StyleDescriptionHelpMore Graphs

This is level 1: equations of circles.

 1) Which of the following is the equation of the circle above?a) $$x^2 + y^2 = 16$$b) $$x^2 + y^2 = 4$$c) $$x^2 + y^2 = 8$$ 2) The equation of a circle is $$x^2 + y^2 = 49$$. What is the radius of the circle? 3) The equation of a circle is $$x^2 + y^2 = 56.25$$. What is the radius of the circle? 4) Which of the following is the equation of a circle with centre at the origin and a radius of 11 units?a) $$x^2 + y^2 = 121$$b) $$x^2 + y^2 = 11$$c) $$x^2 + y^2 = 22$$ 5) The equation of a circle is $$3x^2 + 3y^2 = 75$$. What is the radius of the circle? 6) The equation of a circle is $$9x^2 + 9y^2 = 576$$. What is the radius of the circle? 7) Which of the following is the equation of a circle with centre at the origin and a radius of 9 units?a) $$2x^2 + 2y^2 = 81$$b) $$x^2 + y^2 = 9$$c) $$2x^2 + 2y^2 = 162$$ 8) Which of the following is the equation of a circle with centre at the origin which passes through the point (3,4)?a) $$10x^2 + 10y^2 = 25$$b) $$5x^2 + 5y^2 = 125$$c) $$15x^2 + 15y^2 = 25$$ 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) $$x^2 + y^2 = 8$$ 10) The equation of a circle is given as $$y^2 = (3+x)(3-x)$$. What is the radius of the circle?
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This is Circle Equations level 1. You can also try:
Level 2

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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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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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