Conics Circles on a coordinate plane

Hey guys its Chris here, i will be blogging about graphing circles on a coordinate place and be talking about the general form of a circle.

Standard form of a circle = X² + y² = r²

^{Transformed equation of a circle =} (x – h)²  + (y –k)²   = r^{2                   *( read h,k values as opposite)*}

^{General form for a circle =} Ax² + By² + Cx + Dy + E = 0  *( A and B values are the same separated by a + sign)*

Example 1:

Identify the center and radius of each. Then sketch the graph.

 1) (x-3)² + (y+1)² = 25

 Step 1: Identify that this is a transformed equation of a circle.

Step 2: Read h.k values as opposite leaving us with our center point at (3,-1).

Step 3: Plot the center point on the graph.

Step 4: Find the radius by taking the square root of 25 which will give you 5. you will now move 5 points from the center point up, down, left and right which will give you the final graph of the equation.

ANSWER:

                                                                                                                        

^{Example 2:} 

Identify the center and radius of each. Then sketch the graph.

 X² + y² + 8x -6y + 21 =0

Step 1: arrange common terms in order move term to other side.

 X² + 8x + y² -6y = -21

      b = 8         b = -6

Step 2: Divide the b values by 2 and square them then add the x b value to the x terms and the y b value to the y terms and both values to the other side of the equation.

X² + 8x + 16 + y² – 6y + 9 = -21 + 16 + 9

Step 3: Factor the equation.

(x + 4)² + (y – 3)² = 4

Step 4: Find Center point: (-4,3).       

             Find Radius: R= 2