Question

Drag each tile to the correct box

Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths.
*+y2 - 2x + 2y-1=0
x2 + y2 - 4x + 4y - 10 = 0
x2 + y2 - 8x - by - 20 = 0
4x2 + 4y2 + 16x + 24y - 40 = 0
502 +5y2 - 20x + 30y + 40 = 0
232 2y2 - 28x - 32y - 8 = 0
x2 + y2 + 128-29-9=0

Answer 1

To arrange the circles in ascending order of their radius lengths, compare the coefficients of the quadratic terms in each equation.

Step-by-step explanation:

To arrange the circles (represented by their equations in general form) in ascending order of their radius lengths, we need to compare the coefficients of the quadratic terms of each equation. The greater the coefficient, the larger the radius.

1. x² + y² - 8x - by - 20 = 0: This equation represents the largest circle since the quadratic term has the greatest coefficient.
2. x² + y² - 4x + 4y - 10 = 0: This equation represents the second largest circle.
3. x² - 2x + 2y - 1 = 0: This equation represents the third largest circle.
4. 4x² + 4y² + 16x + 24y - 40 = 0: This equation represents the fourth largest circle.
5. 502 + 5y² - 20x + 30y + 40 = 0: This equation represents the fifth largest circle.
6. 232 2y² - 28x - 32y - 8 = 0: This equation represents the smallest circle since the quadratic term has the smallest coefficient.

Answer 2

x2 + y2 − 2x + 2y − 1 = 0

↓

5x2 + 5y2 − 20x + 30y + 40 = 0

↓

x2 + y2 − 4x + 4y − 10 = 0

↓

4x2 + 4y2 + 16x + 24y − 40 = 0

↓

x2 + y2 − 8x − 6y − 20 = 0

↓

x2 + y2 + 12x − 2y − 9 = 0

↓

2x2 + 2y2 − 28x − 32y − 8 = 0

Hope this helps!

Step-by-step explanation: