Match the circle equations in general form with their corresponding equations in standard form. x2 + y2 − 4x + 12y − 20 = 0 (x − 6)2 + (y − 4)2 = 56 x2 + y2 + 6x − 8y − 10 = 0 (x − 2)2 + (y + 6)2 = 60 3x2 + 3y2 + 12x + 18y − 15 = 0 (x + 2)2 + (y + 3)2 = 18 5x2 + 5y2 − 10x + 20y − 30 = 0 (x + 1)2 + (y − 6)2 = 46 2x2 + 2y2 − 24x − 16y − 8 = 0 x2 + y2 + 2x − 12y − 9 = 0
2 answers:
Answer:
x2 + y2<em> </em>− 4x + 12y − 20 = 0 and (x-2)2 + (y+6)2 = 60
x2 + y2 + 2x - 12y - 9 = 0 and (x + 1)2 + (y - 6)2 = 46
2x2 + 2y2 - 24x - 16y - 8 = 0 and (x - 6)2 + (y - 4)2 = 56
3x2 +3y2 + 12x +18y - 15 = 0 and (x + 2)2 + (y + 3)2 = 18
I got a 100 on PLATO.
Step-by-step explanation:
The equation form of a circle is (x - a)² + (y - b)² = r² Equation 1: x² - 4x + y² + 12y - 20 = 0 ⇒ use the completing the square method for x² - 4x and y² + 12y x² - 4x = (x - 2)² - 4 y² + 12y = (y + 6)² - 36 Put them back together, we have (x - 2)² - 4 + (y + 6)² - 36 - 20 = 0 (x - 2)² + (y + 6)² -4 - 36 - 20 = 0 (x - 2)² + (y + 6)² - 60 = 0 (x - 2)² + (y + 6)² = 60 Equation 2: x² + y² + 6x - 8y - 10 = 0 (x² + 6x) + (y² - 8y) -10 = 0 (x + 3)² - 9 + (y - 4)² -16 - 10 = 0 (x + 3)² + (y - 4)² - 9 - 16 - 10 = 0 (x + 3)² + (y - 4)² - 35 = 0 (x + 3)² + (y - 4)² = 35 Equation 3: 3x² + 12x + 3y² +18y - 15 = 0 3 [x² + 4x + y² + 6y - 5] = 0 x² + 4x + y² + 6y - 5 = 0 (x² + 4x) + (y² + 6y) - 5 = 0 (x + 2)² - 4 + (y + 3)² - 9 - 5 = 0 (x + 2)² + (y + 3)² - 4 - 9 -5 = 0 (x + 2)² + (y + 3)² - 18 = 0 (x + 2)² + (y + 3)² = 18 Equation 4: 5x² + 5y² - 10x + 20y - 30 = 0 5 [x² + y² - 2x + 4y - 6] = 0 x² + y² - 2x + 4y - 6 = 0 (x² - 2x) + (y² + 4y) - 6 = 0 (x - 1)² - 2 + (y + 2)² - 4 - 6 =0 (x - 1)² + (y + 2)² - 2 - 4 - 6 = 0 (x - 1)² + (y + 2)² - 12 = 0 (x - 1)² + (y + 2)² = 12 Equation 5: 2x² + 2y² - 24x - 16y -8 = 0 2 [x² + y² - 12x - 8y - 4] = 0 x² + y² - 12x - 8y - 4 = 0 (x² - 12x) + (y² - 8y) - 4 = 0 (x - 6)² - 36 + (y - 4)² - 16 - 4 = 0 (x - 6)² + (y - 4)² -36 - 16 - 4 = 0 (x - 6)² + (y - 4)² - 56 = 0 (x - 6)² + (y - 4)² = 56 Equation 6: x² + y² + 2x - 12y - 9 = 0 (x² + 2x) + (y² - 12y) - 9 = 0 (x + 1)² - 1 + (y - 6)² - 36 - 9 = 0 (x + 1)² + (y - 6)² - 1 - 36 - 9 = 0 (x + 1)² + (y - 6)² - 46 = 0 (x + 1)² + (y - 6)² = 46
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