Write the standard equation and identify if parabola, circle, ellipse and hyperbola
1.2x^+3y^2 - 32x +6y +55=0
2. 2x^2 - 3y^2 - 16x - 30y - 49=0
3. 2x^2 +20x +8y=-34
4. x^2 +2x +y^2 = 55 +10y
1.2x^+3y^2 - 32x +6y +55=0
2. 2x^2 - 3y^2 - 16x - 30y - 49=0
3. 2x^2 +20x +8y=-34
4. x^2 +2x +y^2 = 55 +10y
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Answer:
1. ellipse 2. hyperbola 3. parabola 4. circle
Step-by-step explanation:
1.) 2x² + 3y² - 32x + 6y + 55 = 0
2x² - 32x + 3y² + 6y = -55
2(x² - 16x + 64) + 3(y² + 2y + 1) = -55 + 2(64) + 3(1)
2(x - 8)² + 3(y + 1)² = 76
(x - 8)²/38 + (y + 1)²/ (76/3) = 1 (ELLIPSE)
2.) 2x² - 3y² - 16x -30y - 49 = 0
2x² - 16x - 3y² - 30 y = 49
2(x² - 8x + 16) - 3(y² + 10y + 25) = 49 + 2(16) - 3(25)
2(x - 4)² - 3(y + 5)² = 6
(x - 4)²/3 - (y + 5)²/2 = 1 (HYPERBOLA)
3.) 2x² + 20x + 8y = -34
x² + 10x + 4y = -17
(x + 5)² + 4y = -17 + 25
(x + 5)² = -4y + 8
(x + 5)² = -4(y - 2) (PARABOLA)
4.) x² + 2x + y² = 55 + 10y
x² + 2x + y² - 10y = 55
(x + 1)² + (y - 5)² = 55 + 1 + 25
(x + 1)² + (y - 5)² = 81 (CIRCLE)