The equation of tangent to the circle x^2+y^2=r^2 is y=mx+c ,then the point of contact of the circle and the tangent is?
2 Answers
See below.
Explanation:
The point of contact can be found by equating the equations together. This will find a value that is common to both equations and consequently will be the point or points of contact.
So we have
rearranging:
Tangent line:
Point of contact:
where,
Explanation:
Let, the Line
Clearly,
From Geometry, we know that, in a circle, the
the centre to a tgt. equals the radius.
Recall that, the
Utilising these facts, we have,
Hence, the tgt.
If
So,
To find the eqn. of
its slope is
Solving
Therefore, the pt. of contact is,
Enjoy Maths.!