Let y = mx + c is the equation of the tangents.
It passes from (1,0). So m = -c.
Condition for a straight line to be tangent to a circle of radius a is
So
Here the value of m is imaginary. So there is no tangent from the given point.
Deduce the equations of the tangents to the circle from the point (1,0).
The equation of the circle
my problem is that the are no tangents to the circle through the point. I got the polar of the point, but i don't know how to continue.
Thanks
This is the full question:
Find the equation of the pair of lies that pass through the origin and through the points of intersection of the line and the circle . If these lines are perpendicular find . For what value of [/tex]\lambda[/tex] do these lines coincide? Deduce the equations of the tangents to the circle from the point (1,0).
This is the last part. I've done all the rest. For when the lines coincide i do have a small problem.
The equation of the line pair is:
If the lines coincide then
I worked it out and found
Answer says
These two are the problems I have
What I mean is that, the given straight line passes through a fixed point (-1, 0). Two lines from the origin will co-inside only when the given line passes through the origin.
The point (1, 0) lies inside the circle. So you cannot draw a tangent from that point to the circle. You have to check the problem.