The equation you provided is a general form of an ellipse equation. To identify the graph, we need to rewrite it in standard form. Here are the steps:

1. Group the x terms and y terms together: (4x^2 - 8x) + (y^2 + 4y) = 9
2. Complete the square for the x terms and y terms. To do this, take the coefficient of the x (or y) term, divide by 2, and square it. Add this number to both sides of the equation.

For the x terms: 4(x^2 - 2x + 1) - 4 = 9 becomes 4(x - 1)^2 = 9 + 4
For the y terms: (y^2 + 4y + 4) - 4 = 9 becomes (y + 2)^2 = 9 + 4

3. Substitute back into the equation: 4(x - 1)^2 + (y + 2)^2 = 13
4. Divide through by 13 to get the equation in standard form: (x - 1)^2 / (13/4) + (y + 2)^2 / 13 = 1

This is the standard form of the ellipse equation, where the center is at (1, -2), the semi-major axis is sqrt(13), and the semi-minor axis is sqrt(13/4). The graph would be an ellipse centered at (1, -2) with the given semi-axes.

Question

The equation you provided is a general form of an ellipse equation. To identify the graph, we need to rewrite it in standard form. Here are the steps:

1. Group the x terms and y terms together: (4x^2 - 8x) + (y^2 + 4y) = 9
2. Complete the square for the x terms and y terms. To do this, take the coefficient of the x (or y) term, divide by 2, and square it. Add this number to both sides of the equation.

For the x terms: 4(x^2 - 2x + 1) - 4 = 9 becomes 4(x - 1)^2 = 9 + 4
   For the y terms: (y^2 + 4y + 4) - 4 = 9 becomes (y + 2)^2 = 9 + 4

3. Substitute back into the equation: 4(x - 1)^2 + (y + 2)^2 = 13
4. Divide through by 13 to get the equation in standard form: (x - 1)^2 / (13/4) + (y + 2)^2 / 13 = 1

This is the standard form of the ellipse equation, where the center is at (1, -2), the semi-major axis is sqrt(13), and the semi-minor axis is sqrt(13/4). The graph would be an ellipse centered at (1, -2) with the given semi-axes.

Knowee AI · Accepted Answer

The equation you provided is a general form of an ellipse equation. To identify the graph, we need to rewrite it in standard form. Here are the steps:

1. Group the x terms and y terms together: (4x^2 - 8x) + (y^2 + 4y) = 9
2. Complete the square for the x terms and y terms. To do this, take the coefficient of the x (or y) term, divide by 2, and square it. Add this number to both sides of the equation.

For the x terms: 4(x^2 - 2x + 1) - 4 = 9 becomes 4(x - 1)^2 = 9 + 4
   For the y terms: (y^2 + 4y + 4) - 4 = 9 becomes (y + 2)^2 = 9 + 4

3. Substitute back into the equation: 4(x - 1)^2 + (y + 2)^2 = 13
4. Divide through by 13 to get the equation in standard form: (x - 1)^2 / (13/4) + (y + 2)^2 / 13 = 1

This is the standard form of the ellipse equation, where the center is at (1, -2), the semi-major axis is sqrt(13), and the semi-minor axis is sqrt(13/4). The graph would be an ellipse centered at (1, -2) with the given semi-axes.

Which of the following represents a graph of 4𝑥2 + 𝑦2 − 8𝑥 + 4𝑦 − 9 = 0

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