Question

Activity 6: Turn me into a general!

1. (X-2)²+(Y-4)²=36
2. (X+4)²+(Y-9)²=144
3. (X-6)²+(Y-1)²=81
4. (X-8)²+(Y+7)²=225
5. X²+(Y-5)²=36
6. (X-7)²+Y²=64
7. X²+(Y+2)²=49
8. (X+2)²+Y²=100
9. (X-5)²+(Y-5)²=27
10. (X+4)²+(Y+4)²=32

Answer 1

Answer:

1)by taking squareroot

x-2+y-4=6

x+y-6=6

x+y=0

Answer 2

Hi,

Answer:

The required equation of a circle in general form is:

x² + y² + ax + by + c = 0

Where a, b, c are constants

Based on the formula we will solve each of the equations:

1. (X-2)² + (Y-4)² = 36

⇒ (x² – 4x + 4) + (y² – 8y + 16) = 36

⇒ x² + y² – 4x – 8y + 4 +16 – 36 = 0

⇒ x² + y² – 4x – 8y - 16 = 0

2. (X+4)² + (Y-9)² = 144

⇒ (x² + 8x + 16) + (y² – 18y + 81) = 144

⇒ x² + y² + 8x – 18y + 16 + 81 – 144 = 0

⇒ x² + y² + 8x – 18y - 47 = 0

3. (X-6)² + (Y-1)² = 81

⇒ (x² – 12x + 36) + (y² – 2y + 1) = 81

⇒ x² + y² – 12x – 2y + 36 + 1 – 81 = 0

⇒ x² + y² – 12x – 2y – 44 = 0

4. (X-8)² + (Y+7)² = 225

⇒ (x² – 16x + 64) + (y² + 14y + 49) = 225

⇒ x² + y² - 16x + 14y + 64 + 49 – 225 = 0

⇒ x² + y² – 16x + 14y – 112 = 0

5. X² + (Y-5)² = 36

⇒ x² + (y² – 10y + 25) = 36

⇒ x² + y² – 10y + 25 - 36 = 0

⇒ x² + y² – 10y – 11 = 0

⇒ x² + y² + (0)x – 10y – 11 = 0

6. (X-7)² + Y² = 64

⇒ (x² – 14x + 49) + y² = 64

⇒ x² + y² – 14x + 49 – 64 = 0

⇒ x² + y² – 14x – 15 = 0

⇒ x² + y² – 14x + (0)y – 15 = 0

7. X² + (Y+2)²=49

⇒ x² + (y² + 4y + 4) = 49

⇒ x² + y² + 4y + 4 – 49 = 0  

⇒ x² + y² + 4y – 45 = 0

⇒ x² + y² + (0)x + 4y – 45 = 0

8. (X+2)² + Y²=100

⇒ (x² + 4x + 4) + y² = 100

⇒ x² + y² + 4x + 4 – 100 = 0

⇒ x² + y² + 4x – 96 = 0

⇒ x² + y² + 4x + (0)y – 96 = 0

9. (X-5)² + (Y-5)²=27

⇒ (x² – 10x + 25) + (y² – 10y + 25) = 27

⇒ x² + y² – 10x – 10y + 25 + 25 – 27 = 0

⇒ x² + y² – 10x – 10y - 50 = 0

10. (X+4)² + (Y+4)²=32

⇒ (x² + 8x + 16) + (y² + 8y + 16) = 32

⇒ x² + y² + 8x + 8y + 16 + 16 – 32 = 0  

⇒ x² + y² + 8x + 8y + 16 + 16 – 32 = 0  

⇒ x² + y² + 8x + 8y + 0 = 0  

Hope this is helpful!!!!