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Name LESSON Date Class Practice B 106 Identifying Conic Sections Identify the conic section that each equation represents. 1 1. X 1 y 8 2 4 y 7 × 9 2 2. 1 2 2 2 6 Parabola 4. Y 5 × 9 2 1 2 2 2 3.
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How to fill out 10 6 identifying conic
How to fill out 10 6 identifying conic:
01
Start by understanding the given problem: 10 6 identifying conic means identifying the conic section represented by the equation 10x^2 + 6y^2 = 1.
02
Begin by analyzing the coefficients of the x^2 and y^2 terms. In this case, the coefficient of x^2 is 10 and the coefficient of y^2 is 6.
03
Compare the coefficients to the standard forms of conic sections to determine the type of conic section:
3.1
If both coefficients are positive and equal, it indicates an ellipse.
3.2
If both coefficients are positive but unequal, it indicates an ellipse with a major axis along the x-axis.
3.3
If both coefficients are negative and equal, it indicates an ellipse with a major axis along the y-axis.
3.4
If one coefficient is positive and the other is negative, it indicates a hyperbola.
3.5
If the coefficient of x^2 or y^2 is zero, it indicates a parabola.
04
Apply the above rules to the given problem. Since the coefficient of x^2 is positive (10) and the coefficient of y^2 is positive (6), it is an ellipse.
05
Determine the orientation of the ellipse by comparing the coefficients. In this case, since the coefficient of x^2 (10) is greater than the coefficient of y^2 (6), the major axis is along the x-axis.
06
Fill out the identifying conic form by stating "The given equation 10x^2 + 6y^2 = 1 represents an ellipse with a major axis along the x-axis."
Who needs 10 6 identifying conic?
01
Students studying conic sections in mathematics.
02
Engineers and architects who need to analyze and design curves and shapes in their work.
03
Professionals working in fields such as astronomy or physics, where conic sections are used to describe elliptical orbits or gravitational forces.
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