THE EQUATION OF THE CIRCLE

HANDOUT FOR GRADE 10 ENRICHED

By Alex Pintilie

 

Together:

 

1)      Write the equation of the circle with centre (0,0) and passing through (3, - 4).

2)      Write the equation of the circle with centre ( - 2, 3) and radius 5.

3)      Write the equation of the circle with centre (1, -2) and passing through (4, - 6).

4)      State the radius and the coordinates of the centre of the circle of equation:

a.       x² + y² + 6x – 27 = 0

b.      x² + y² + 10x – 8y + 16 = 0

5)      Find the x- and the y- intercepts of the circle of equation: (x-5)²+(y+1)²=50.  Draw the circle.

6)      A circle with centre on the y-axis passes through A(-3, 0) and B(5,4). Write the equation of the circle. Draw the circle and indicate on the figure the points A and B.

7)      For the circle given by x²+y² = 34

a.       show that the line segment from P(-5,3) to Q(3,5) is a chord of the circle;

b.      find the midpoint M of the chord;

c.       show that MO _┴ PQ.

 

Homework:

 

1)      Write the equation of the circle with centre (0,0) and passing through (- 2 , - 5).

2)      Write the equation of the circle with centre ( 4, 3) and radius 2.

3)      Write the equation of the circle with centre (3, -2) and passing through (5, 1).

4)      State the radius and the coordinates of the centre of the circle of equation:

a.       x² + y² – 4y – 5 = 0

b.      x² + y² – 4x + 2y – 4  = 0

5)      Find the x- and the y- intercepts of the circle of equation: (x+4)²+(y-3)²=25.  Draw the circle.

6)      A circle with centre on the x-axis passes through A(6, 4) and B(-1,3). Write the equation of the circle. Draw the circle and indicate on the figure the points A and B.

7)      Given the circle x²+y²+8x – 6y = 0,

a.       show that the circle passes through O(0,0),

b.      if O is one end of the diameter of the circle, find the other end P,

c.       pick any other point Q on the circle and show that the angle OQP = 90^o

8)      (This is a tough one.) A circle with centre on the line x + 2y = 4 passes through the points A(6,9) and B(12, -9). Write the equation of the circle.

 

Answers: 1) x²+y²=29              2) (x-4)²+(y-3)²=4       3) (x-3)²+(y+2)²=13

4) a) r = 1, C(0,2)        b) r=3, C(2,-1)             5) x= 0, x= -8; y = 0, y = 6

6)  (x-3)² + y² = 25      7) b) P(-8,6)                8) (x-6)² + (y+1)² = 100