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what is the method to get equation of two tangent from a point outside the cicle to given circle???

what is the method to get equation of two tangent from a point outside the cicle to given circle???


 

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1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Amit,

Consider y=mx+c be the line which is a tangent.

For this to be a tangent to any circle,

Make the sub, y=mx+c in the circle equation. You will get a quad in x, which should have only one solution.

And hence the disciminant of that Quad = 0.

So you will get a relation between c and m------ (1)

Also the line should pass through a point (x1,y1). so y1 = mx1+c ---------(2) {Another relation between m and c)

So from 1 and 2, solve for m and c.

Solving between m and c, you should get a quad in m, and hence two values of m, and hence two tangents can be drawn from a point.

And hence you get the equations of the lines.

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).

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