Math Problem Statement
Given the ellipse
(
x
+
5
)
2
25
+
(
y
−
3
)
2
9
1
Find the center point:
Give the vertices:
Give the endpoints of the minor axis:
Draw the graph of the ellipse.
Solution
Here is the graph of the ellipse with the center, vertices, and endpoints of the minor axis highlighted:
- The center is at .
- The vertices are at and .
- The endpoints of the minor axis are at and .
Would you like more details on any of these points or further explanation?
Here are five related questions you might find helpful:
- How do you determine the eccentricity of an ellipse?
- What is the formula for the area of an ellipse?
- How does changing the values of and affect the shape of the ellipse?
- How can we rotate an ellipse around its center?
- What are some applications of ellipses in physics or astronomy?
Tip: The length of the major and minor axes are twice the values of and respectively.
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Math Problem Analysis
Mathematical Concepts
Analytic Geometry
Ellipses
Conic Sections
Formulas
Standard form of an ellipse: (x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
Center of an ellipse: (h, k)
Vertices of an ellipse: (h ± a, k)
Endpoints of the minor axis: (h, k ± b)
Theorems
The Pythagorean Theorem (for deriving the relation between axes and foci)
Properties of ellipses in conic sections
Suitable Grade Level
Grades 10-12
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