Math 10 lesson - Circles

1. EQUATIONS OF
A CIRCLE
TRANSFORMING EQUATION OF A
CIRCLE IN GENERAL FORM TO
STANDARD FORM

2. RECALL

3. ILLUSTRATIVE EXAMPLE
•Convert the equation of a circle in
general form to standard form
x2 + y2 + 7x + 3y − 2 = 0

4. Seatwork: Convert the equation of a circle in
general form below to standard form.
1.x2 + y2 + 2x + 4y − 4 = 0
2.x2 + y2 + 3x + 5y − 4 = 0
3.3x2 + 3y2 − 30x + 6y + 51 = 0

5. IDENTIFYING THE COORDINATES
OF THE CENTER OF A CIRCLE AND
ITS RADIUS

6. ILLUSTRATIVE EXAMPLE:
• The general equation of a circle is given, Transform the
equation in standard form then, give the coordinates of the
center and the radius.
1. x2 + y2 + 2x – 2y – 16 = 0
2. 4x2+4y2-20x+12y-4=0

7. SEATWORK:
• The general equation of a circle is given, Transform the
equation in standard form then, give the coordinates of the
center and the radius.
1. x2 + y2 – 14x + 6y + 48 = 0
2. 2x2 + 2y2 + 8x + 12y – 6 = 0

8. Find the center and the radius of the circle
given its equation
Equation in general form Center Radius
a. x2 + y2 = 81
b. (x – 7)2 + (y + 7)2 = 64
c. x2 + (y+2)2= 16
d. x2 + y2 + 4x –4y = 100
e. x2 + y2-10y+25x =36