Ellipse: Problems with Solutions

Horizontal ellipse
Horizontal Ellipse

Vertical ellipse
Vertical Ellipse

Problem 1
The center and foci of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ are:
Problem 2
The vertices, co-vertices and eccentricity of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ are:
Problem 3
The center and foci of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$ are:
Problem 4
The vertices, co-vertices and eccentricity of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$ are:
Problem 5
What are the center and foci of the ellipse $36(x+2)^{2}+(y+4)^{2}=72$ ?
Problem 6
The equation of an ellipse with vertices $(0,\pm 7)$ and foci $(0,\pm 3)$ are:
Problem 7
The equation of an ellipse with vertices at $(0,\pm 3)$ and co-vertices at $(\pm 1,0)$ is:
Problem 8
What is the equation of an ellipse if its vertices are $(1,-6),(1,2)$ and co-vertices are $(-2,-2),(4,-2)$?
Problem 9
Given an ellipse with foci at $(0,\pm \sqrt{5})$ and the length of the major axis is $16$.
Find the equation of the ellipse.
Problem 10
What is the equation of an ellipse with center at $(1,3)$, focus at $(1,0)$ and vertex at $(1,-1)$?

Problem 11
Given an ellipse with center at $(5,-7)$, length of the vertical major axis $8$ and length of the minor axis $6$.
What is the equation of the ellipse?
Problem 12
Given an ellipse with vertices at $(2,4),(13,4)$ and focus at $(4,4)$. What is its equation?
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