For the ellipse given by the equation $$4x^2+9y^2-36=0$$ , what are the center, foci, and vertices?

Center: (0, 0), Vertices: (±3, 0) and (0, ±2), foci: $$(\pm\sqrt[]{5},0)$$

Center: (0, 0), Vertices: (±2, 0) and (0, ±3), foci: $$\left(\pm\sqrt[]{13},0\right)$$

Center: (0, 0), Vertices: (±6, 0) and (0, ±4), foci: $$(\pm\sqrt[]{10},0)$$

Center: (0, 0), Vertices: (±4, 0) and (0, ±3), Foci: $$(\pm\sqrt[]{7},0)$$

What are the center, foci, and vertices for the ellipse described by the equation $$25x^2+16y^2-400=0?$$

Center: (0, 0), Vertices: (±5, 0) and (0, ±4), Foci: $$\left(\pm\sqrt[]{7},0\right)$$

Center: (0, 0), Vertices: (±6, 0) and (0, ±3), Foci: $$\left(\pm\sqrt[]{12},0\right)\ $$

Center: (0, 0), Vertices: (±5, 0) and (0, ±6), Foci: $$\left(\pm\sqrt[]{6},0\right)$$

Center: (0, 0), Vertices: (±4, 0) and (0, ±5), Foci: $$\left(\pm\sqrt[]{9},0\right)$$

Identify the center, foci, and vertices for the ellipse given by $$9x^2+25y^2-225=0$$ .

Center: (0, 0), Vertices: (±3, 0) and (0, ±5), Foci: $$\left(\pm\sqrt[]{16},0\right)$$

Center: (0, 0), Vertices: (±5, 0) and (0, ±3), Foci: $$\left(\pm\sqrt[]{9},0\right)$$

Center: (0, 0), Vertices: (±4, 0) and (0, ±6), Foci: $$\left(\pm\sqrt[]{7},0\right)$$

Center: (0, 0), Vertices: (±6, 0) and (0, ±4), Foci: $$\left(\pm\sqrt[]{10},0\right)$$

From the equation of the ellipse $$36x^2+64y^2-2304=0$$ , find the center, foci, and vertices.

Center: (0, 0), Vertices: (±8, 0) and (0, ±6), Foci: $$\left(\pm\sqrt[]{28},0\right)$$

Center: (0, 0), Vertices: (±10, 0) and (0, ±4), Foci: $$\left(\pm\sqrt[]{20},0\right)$$

Center: (0, 0), Vertices: (±4, 0) and (0, ±10), Foci: $$\left(\pm\sqrt[]{12},0\right)$$

Center: (0, 0), Vertices: (±6, 0) and (0, ±8), Foci: $$\left(\pm\sqrt[]{16},0\right)$$

Given the ellipse defined by the equation $$16x^2+9y^2-144=0$$ , calculate the center, foci, and vertices.

Center: (0, 0), Vertices: (0, ±4) and (±3, 0), Foci: $$\left(\pm\sqrt[]{13},0\right)$$

Center: (0, 0), Vertices: (±4, 0) and (0, ±6), Foci: $$\left(\pm\sqrt[]{10},0\right)$$

Center: (0, 0), Vertices: (±3, 0) and (0, ±4), Foci: $$\left(\pm\sqrt[]{5},0\right)$$

Center: (0, 0), Vertices: (0, ±3) and (±4, 0), Foci: $$\left(\pm\sqrt[]{7},0\right)$$

For the ellipse given by the equation $$9\left(x-2\right)^2+4\left(y+3\right)^2-36=0$$ , what are the center, foci and vertices?

Center: (2, -3), Vertices: (2 ± 2, -3) and (2, -3 ± 3), Foci: $$\left(2\pm\sqrt[]{5},-3\right)$$

Center: (2, -3), Vertices: (0, -3) and (2, 0), Foci: $$\left(\pm4,\pm5\right)$$

Center: (2, -3), Vertices: (2 ± 3, -3) and (2, -3 ± 2), Foci: $$\left(2\pm\sqrt[]{2},-3\right)$$

Center: (2, -3), Vertices: (2 ± 3, -3) and (2, -3 ± 1), Foci: $$\left(2\pm\sqrt[]{6},-3\right)$$

What are the center, foci, and vertices for the ellipse described by the equation $$16\left(x+1\right)^2+25\left(y-4\right)^2-400=0$$

Center: (-1, 4), Vertices: (-1 ± 5, 4) and (-1, 4 ± 4), Foci: (-1 ± 3, 4)

Center: (-1, 4), Vertices: (-1 ± 5, 4) and (-1, 4 ± 3), Foci: (-1 ± 4, 4)

Center: (-1, 4), Vertices: (-1 ± 4, 4) and (-1, 4 ± 5), Foci: (-1 ± 5, 4)

Center: (-1, 4), Vertices: (-1 ± 4, 4) and (-1, 4 ± 5), Foci: $$\left(-1\pm\sqrt[]{7},4\right)$$

Identify the center, foci, and vertices for the ellipse given by $$36\left(x-3\right)^2+64\left(y+2\right)^2-2304=0.$$

Center: (3, -2), Vertices: (3 ± 4, -2) and (3, -2 ± 5), Foci:(3 ± 6, -2)

Center: (3, -2), Vertices: (3 ± 8, -2) and (3, -2 ± 5), Foci: $$\left(3\pm\sqrt[]{20},\ -2\right)$$

Center: (3, -2), Vertices: (3 ± 6, -2) and (3, -2 ± 8), Foci: (3 ± 5, -2)

Center: (3, -2), Vertices: (3 ± 6, -2) and (3, -2 ± 4), Foci: $$\left(3\pm\sqrt[]{36},\ -2\right)$$

From the equation of the ellipse $$25\left(y-1\right)^2+9\left(x+2\right)^2-225=0,$$ find the center, foci, and vertices.

Center: (-2, 1), Vertices: (-2 ± 5, 1) and (-2, 1 ± 3), Foci: $$\left(-2,\ 1\pm\sqrt[]{16}\right)$$

Center: (-2, 1), Vertices: (-2 ± 3, 1) and (-2, 1 ± 5), Foci: (-2, 1 ± 4)

Center: (-2, 1), Vertices: (-2 ± 5, 1) and (-2, 1 ± 4), Foci: (-2 ± 3, 1)

Center: (-2, 1), Vertices: (-2 ± 4, 1) and (-2, 1 ± 5), Foci: (-2 ± 6, 1)

Given the ellipse defined by the equation $$64\left(y+1\right)^2+36\left(x-5\right)^2-576=0,$$ calculate the center, foci, and vertices.

Center: (5, -1), Vertices: (5, -1 ± 4) and (5 ± 6, -1), Foci: (5 ± 3, -1)

a) Center: (5, -1), Vertices: (5 ± 3, -1) and (5, -1 ± 4), Foci: $$\left(5,\ -1\pm\sqrt[]{5}\right)$$

Center: (5, -1), Vertices: (5 ± 4, -1) and (5, -1 ± 6), Foci: $$\left(5,\ -1\pm\sqrt[]{7}\right)$$

Center: (5, -1), Vertices: (5 ± 4, -1) and (5, -1 ± 8), Foci: $$\left(5\pm\sqrt[]{8},\ -1\right)$$

Analytic Geometry ( Ellipse and Circle)

Authored by HAFIZAH Moe

Mathematics

9th - 12th Grade

Used 1+ times

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MULTIPLE CHOICE QUESTION

1 min • 5 pts

An ellipse has foci at (±6, 0) and vertices at (±10, 0). What is the equation of the ellipse?

MULTIPLE CHOICE QUESTION

1 min • 5 pts

Find the equation of an ellipse with foci at (±4, 0) and vertices at (±8, 0).

MULTIPLE CHOICE QUESTION

1 min • 5 pts

Given the foci of an ellipse at (±5, 0) and vertices at (±8, 0), Determine the equation of the ellipse.

MULTIPLE CHOICE QUESTION

1 min • 5 pts

MULTIPLE CHOICE QUESTION

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MULTIPLE CHOICE QUESTION

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MULTIPLE CHOICE QUESTION

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