How to use this applet:
Click the instructions button on the applet for instructions on use.Notes on the maths used in the applet:
To get the quation of the tangent to a circle x2 + y2 = a2 at the point (x1,y1) on the circle:
Use the equation:
xx1 + yy1 = a2
To get the equation of the tangent to a circle from a point not on the circle:
You must use the perpindicular distance formula (the perpindicular distance from the tangent to the centre of the circle is equal to the radius). The tangent has the equation
y - y1 = m(x - x 1). First get this equation into the form: ax + by + c = 0 using the given point (x1,y1) as one point on the line. If you put this equation into the perpindicular distance formula, with the centre of the circle as the point and make it equal the radius, you should be able to calculate two values for m (the slope).
Putting these values back into the equation:
y - y1 = m(x - x 1), you get two line equations, one for each tangent.
To find length of a tangent from a point to the circle.
First let the end point of the tangent be called p, the centre of the circle be called o, and the point of contact between the circle and the tangent be called t.
Calculate the distance from p to o using the distance formula. Then, by pythagoras you can calculate the length by the following formula:
|pt|2 = |op|2 - |ot|2
