New Century Mathematics (Second Edition) 5B
Name
7 Equations of Circles
Class
(
)
Date
 Section Test 7C
Marks
(§7.3 Intersection of a Straight Line and a Circle)
1.
y
In the figure, G(1 , 3) is the centre of a circle. Find the equation of
the tangent L that passes through P(3 , 5) on the circle.
(4 marks)
P(3 , 5)
L
G(1 , 3)
O
2.
x
The straight line 2x  y  5 = 0 touches the circle x2 + y2  2x  4y + k = 0.
(a) Find the value of k.
(3 marks)
(b) Find the coordinates of the point of contact of the straight line and the circle.
(3 marks)
© Oxford University Press 2015
Section Test 5B07
7.5
3.
Straight line L touches the circle x2 + y2  10x  6y + 29 = 0. L is parallel to the straight
line L1: 2x  y + 1 = 0. Find the two possible equations of L.
4.
(5 marks)
Consider the circle C: x2 + y2 + 7x  3y + 2 = 0 and the straight line L: x  y + 2c = 0.
(a) If C and L do not intersect, find the range of values of c.
(3 marks)
(b) If C and L intersect at two points P and Q, without finding the coordinates of P and Q, express
the coordinates of the mid-point of PQ in terms of c.
(4 marks)
END OF TEST
© Oxford University Press 2015
Section Test 5B07
7.6