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You are here: Home / Category Index / Circles / The Equation Of A Circle
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The Equation Of A Circle - By Brendan Ryan
How to use this applet:The user must enter in the the x and y co-ordinates of the centre point. There is one text field for the x co-ordinate and one for the y co-ordinate. The user may enter in the these co-ordinates in decimal form if required. E.g. X: 5.42
The user must also input the A,B and C values of the equation of the tangent to the circle ( of form AX + BY+ C =0 ). Again these may be in decimal form. E.G. (6.7)X + (7.2)Y + 11.1 = 0
Only when all the information has been entered in the text fields will the "Calculate Equation" button work. When this is pressed the equation of the circle will be calculated and the answer will appear below the "Calculate Equation" button. A representation of the circle will also be given by a graph on the left hand side of the applet.
If the user wishes to create another circle simply press the reset button. This will clear the graph and all text fields. Simply repeat the process
Notes on the maths used in the applet:As we already have the centrre point and the equation of a tangent to the circle the only piece of information we require is the radius of the circle.
We use the fact that the: the Radius = Perpendicular distance from the centre to the tangent.
To calculate this distance we use:
D = AX 1 + BY1 + C divided by
The Square Root of A2 + B2.
(We take the absolute value)
Now that we have the Centre point and the radius, calculating the equation of the circle is easy. We use the formula :
( X – h )2 + (Y – k)2 = r2
Solve this to find the Equation of the Circle
Other useful information: The Graph: The X and Y axis are 'marked in two's' i.e. The markings on the X-axis are : 2, 4, 6, 8....and similarly in the negative direction. This is the same for the Y axis. The scope of the graph is limited so it is advisable that the user keeps the centre point within the range ( -20 < x < +20 ) and (-20 < y < +20 )
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