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Algebra 2: Graphing the Ellipse

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Section 1

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x² + xy + y² + 5y = 1

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Algebra Math

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Mar 1, 2020

Cards (24)

Section 1

(24 cards)

x² + xy + y² + 5y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

(x − 2)²/9 + y² = 1

Front

Back

x² + xy + y² = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

c) πab

Front

What is the area of an ellipse? a) πa² b) πb² c) πab d) πa²/b²

Back

x²/25 + y² = 1

Front

Back

x² − xy + y² −2x +2y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

49x²/25 + y²/9 = 1

Front

Back

(x −3)²/4 + (y+7)²/9 = 1

Front

Back

16x²/9 + 36y²/25 = 1

Front

Remember that another way of writing a numerator is to divide the denominator by its inverse or reciprocal. For example, the number 3 is equivalent to 1/(1/3).

Back

x² + xy + y² + 2x − 2y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

x² + y²/25 = 1

Front

Back

16x² + 25y² = 1

Front

Remember that another way of writing a numerator is to divide the denominator by its inverse or reciprocal. For example, the number 3 is equivalent to 1/(1/3).

Back

7x² − 5xy + y² = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

x² + xy + y² + 2x + 2y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

0.4

Front

The ellipse, x² + y²/25 = 1, is rotated by adding (or subtracting) an xy term. Using the rule that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0, calculate the limit (as a positive decimal) for the value of |B| that gives an ellipse. |B| less than what number gives an ellipse?

Back

c)

Front

Adding an x-term to the ellipse, x² + y²/25 = 1, gives x² + y²/25 + 6x = 1. How does the x-term change the graph? a) The new ellipse has center (3, 0), with minor axis 2√10 b) The new ellipse has center (0, 3), with major axis 2√10 c) The new ellipse has center (-3, 0), with minor axis 2√10 d) The new ellipse has center (0,-3), with major axis 2√10 e) The new ellipse has center (3, 0), with minor axis √10

Back

81x²/36 + 16y²/25 = 1

Front

Remember that another way of writing a numerator is to divide the denominator by its inverse or reciprocal. For example, the number 3 is equivalent to 1/(1/3).

Back

x² + xy + y² − 5y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

36x²/16 + 64y²/49 = 1

Front

Remember that another way of writing a numerator is to divide the denominator by its inverse or reciprocal. For example, the number 3 is equivalent to 1/(1/3).

Back

9x²/64 + 25y²/49 = 1

Front

Remember that another way of writing a numerator is to divide the denominator by its inverse or reciprocal. For example, the number 3 is equivalent to 1/(1/3).

Back

3x² − 3xy + y² = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

x² + xy + y² + 4x = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

x² −xy + y² + 2x + 2y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back

x² − xy + y² −2x −2y = 1

Front

Ellipses that have been rotated contain an xy-term and, in addition, may have an x-term, y-term or both an x-term and a y-term. Remember that the general quadratic equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0 predicts an ellipse if B² − 4AC < 0.

Back