Thread: circle geomtery help

The circle C has centre (5, 2) and passes through the point (7, 3).

(a) Find the length of the diameter of C.




(b) Find an equation for C.


(c) Show that the line y = 2x − 3 is a tangent to C and find the coordinates
of the point of contact.

Need help with question 'c'.

I know that the angle between a tangent and radius is 90 , but how would I show that the product of their gradients is -1, if I dont know the point of contact?

Also how do I find the point were it touches the circle?

Originally Posted by Tweety

The circle C has centre (5, 2) and passes through the point (7, 3).

(a) Find the length of the diameter of C.




(b) Find an equation for C.


(c) Show that the line y = 2x − 3 is a tangent to C and find the coordinates
of the point of contact.

Need help with question 'c'.

I know that the angle between a tangent and radius is 90 , but how would I show that the product of their gradients is -1, if I dont know the point of contact?

Also how do I find the point were it touches the circle?

Here's one approach out of many possible approaches: Show that the two equations





have only one solution.

Originally Posted by mr fantastic

Here's one approach out of many possible approaches: Show that the two equations





have only one solution.

So if I solved this simutaneously, wouldn't that mean that these to equations intersect at that one point, instead of touching?

Originally Posted by Tweety

So if I solved this simutaneously, wouldn't that mean that these to equations intersect at that one point, instead of touching?

If a line intersects a circle at one point then it is tangent to the circle at that point.