Unit 2 Revision Exercise 5

 

The Circle

 

 

1.                   Find the equation of the tangent to the circle x2 + y2 + 2x – 2y – 3 = 0  at the point (0,3)

 

Find the equation of the parallel tangent to this circle.

 

 

 

2.        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


            The above circle has its centre at O(4,2).  A is the point (7,4) and B is the point(7,0) Find:

 

a)       the equation of the tangents AC and BC

b)       the point C

c)       the lengths AC and BC

d)       the area of the triangle ABC

 

 

 

3.                   A circle with radius r touches the y – axis at (0,3).  Show that the equation of this circle is

 

(x-r)2 + (y-3)2 = r2

 

If the circle passes through the point (2,7), find:

 

a)       the value of r

b)       the equation of the circle

c)       the length  of the chord cut off by the x – axis

 

 

4.         Given that the equation   x2 + (mx – 5m)2 = 16  has equal roots, find m.

 

            Hence or otherwise find the equations of the tangents from (5,0) to the circle

 

            x2  + y2  = 16

 

 


5.        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Given that the centre of the above circle is C(4,3) and the radius of the circle is 5, find the coordinates of the intersection of the circle with the axis.

 

Find the equation of the tangents at these three points and show two of these tangents are parallel.

 

Find the fourth point on the circle at which the tangent completes a parallelogram with the three already found.