# 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 2: equations of tangents to circles.

 1) Find the gradient of the radius of the circle $$x^2+y^2=10$$ that meets the circumference at (1,3) 2) Find the gradient of the tangent of the circle $$x^2+y^2=10$$ that touches the circle at (3,1) 3) One of the following options is the equation of a tangent to the circle $$x^2+y^2=16$$. Type in the letter of the correct option.a) $$y=16$$b) $$y=4x$$c) $$y=-4$$d) $$x=8$$ 4) One of the following options is the equation of a tangent to the circle $$x^2+y^2=29$$ at the point (5,2). Type in the letter of the correct option.a) $$y=5x-29$$b) $$2y+5x=29$$c) $$y=x+29$$d) $$y=29x$$ 5) One of the following options is the equation of a tangent to the circle $$x^2+y^2=25$$ at the point (4,3). Type in the letter of the correct option.a) $$3y+4x=25$$b) $$2y+5x=3$$c) $$3y+4x=5$$d) $$y=12x$$ 6) By first finding the equation of the tangent to the circle $$x^2+y^2=40$$ which passes through the point (2,6) determine the x-coordinate of the point where this tangent crosses the x-axis. 7) By first finding the equation of the tangent to the circle $$x^2+y^2=13$$ which passes through the point (-2,3) determine the x-coordinate of the point where this tangent crosses the x-axis. 8) By first finding the equation of the tangent to the circle $$2x^2+2y^2=82$$ which passes through the point (4,5) determine the y-coordinate of the point where this tangent crosses the y-axis.
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This is Circle Equations level 2. You can also try:
Level 1

## 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.

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