The conic that represents the equation 2x² + 3y² = 18 is ellipse
Step-by-step explanation:
The general equation for any conic section is
Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E and F are
constants
1. If B² - 4AC < 0, if a conic exists, it will be either a circle or an ellipse,
if A and C are equal then it is a circle, if not then it is an ellipse
2. If B² - 4AC = 0, if a conic exists, it will be a parabola
3. If B² - 4AC > 0, if a conic exists, it will be a hyperbola
∵ The equation is 2x² + 3y² = 18
- Subtract 18 from both sides
∴ 2x² + 3y² - 18 = 0
∴ A = 2 , B = 0 , C = 3 , D = 0 , E = 0 and F = -18
∵ B² - 4AC = (0)² - 4(2)(3) = -24
∵ -24 < 0
∴ B² - 4AC < 0
∴ The conic is ellipse or circle
∵ A ≠ C
∴ The conic is ellipse
The conic that represents the equation 2x² + 3y² = 18 is ellipse
Learn more:
You can learn more about discriminant in brainly.com/question/8196933
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