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.

Here is the graph of the ellipse with the center, vertices, and endpoints of the minor axis highlighted:

- The center is at \( (-5, 3) \).
- The vertices are at \( (0, 3) \) and \( (-10, 3) \).
- The endpoints of the minor axis are at \( (-5, 6) \) and \( (-5, 0) \).

Would you like more details on any of these points or further explanation?

Here are five related questions you might find helpful:
1. How do you determine the eccentricity of an ellipse?
2. What is the formula for the area of an ellipse?
3. How does changing the values of \( a \) and \( b \) affect the shape of the ellipse?
4. How can we rotate an ellipse around its center?
5. What are some applications of ellipses in physics or astronomy?

**Tip:** The length of the major and minor axes are twice the values of \( a \) and \( b \) respectively.

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, and draw the graph of the ellipse.

Learn how to find the center point, vertices, and endpoints of the minor axis for the ellipse (x + 5)^2 / 25 + (y - 3)^2 / 9 = 1. This problem explores key concepts in analytic geometry and conic sections, perfect for high school students in Grades 10-12.

Math Problem Statement

Given the ellipse
( x + 5 ) 2 25 + ( y − 3 ) 2 9

Solution

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