The equation for an ellipse in standard form is (x-h)²/a² + (y-k)²/b² = 1 for a vertical ellipse, where (h,k) is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis.

1. First, we find the center of the ellipse. The center is the midpoint of the line segment connecting the two vertices. So, the center (h,k) is ((1+1)/2, (7+3)/2) = (1,5).

2. Next, we find 'a', the distance from the center to a vertex. This is half the length of the major axis. The distance between (1,7) and (1,5) is 2, so a = 2.

3. Then, we find 'b', the distance from the center to a co-vertex. This is half the length of the minor axis. But we don't have the co-vertices. However, we know that in an ellipse, a² = b² + c², where c is the distance from the center to a focus. The distance between (1,5) and (1,1) is 4, so c = 4. Solving for b, we get b = sqrt(a² - c²) = sqrt(2² - 4²) = sqrt(4 - 16) = sqrt(-12). But 'b' can't be a complex number, so there seems to be a mistake.

The given points do not form an ellipse because the focus is farther from the center than the vertices are. The focus should be inside the ellipse, but in this case, it's outside. So, it's not possible to find an equation for an ellipse with these points.

Question

The equation for an ellipse in standard form is (x-h)²/a² + (y-k)²/b² = 1 for a vertical ellipse, where (h,k) is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis.

1. First, we find the center of the ellipse. The center is the midpoint of the line segment connecting the two vertices. So, the center (h,k) is ((1+1)/2, (7+3)/2) = (1,5).

2. Next, we find 'a', the distance from the center to a vertex. This is half the length of the major axis. The distance between (1,7) and (1,5) is 2, so a = 2.

3. Then, we find 'b', the distance from the center to a co-vertex. This is half the length of the minor axis. But we don't have the co-vertices. However, we know that in an ellipse, a² = b² + c², where c is the distance from the center to a focus. The distance between (1,5) and (1,1) is 4, so c = 4. Solving for b, we get b = sqrt(a² - c²) = sqrt(2² - 4²) = sqrt(4 - 16) = sqrt(-12). But 'b' can't be a complex number, so there seems to be a mistake.

The given points do not form an ellipse because the focus is farther from the center than the vertices are. The focus should be inside the ellipse, but in this case, it's outside. So, it's not possible to find an equation for an ellipse with these points.

Knowee AI · Accepted Answer

The equation for an ellipse in standard form is (x-h)²/a² + (y-k)²/b² = 1 for a vertical ellipse, where (h,k) is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis.

1. First, we find the center of the ellipse. The center is the midpoint of the line segment connecting the two vertices. So, the center (h,k) is ((1+1)/2, (7+3)/2) = (1,5).

2. Next, we find 'a', the distance from the center to a vertex. This is half the length of the major axis. The distance between (1,7) and (1,5) is 2, so a = 2.

3. Then, we find 'b', the distance from the center to a co-vertex. This is half the length of the minor axis. But we don't have the co-vertices. However, we know that in an ellipse, a² = b² + c², where c is the distance from the center to a focus. The distance between (1,5) and (1,1) is 4, so c = 4. Solving for b, we get b = sqrt(a² - c²) = sqrt(2² - 4²) = sqrt(4 - 16) = sqrt(-12). But 'b' can't be a complex number, so there seems to be a mistake.

The given points do not form an ellipse because the focus is farther from the center than the vertices are. The focus should be inside the ellipse, but in this case, it's outside. So, it's not possible to find an equation for an ellipse with these points.

Choose the correct equation for the ellipse with vertices (1,7) and (1, 3) and focus (1, 1)

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Choose the correct equation for the ellipse with vertices (1,7) and (1, 3) and focus (1, 1)

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