To find: The equation of an ellipse with focus (−5,0) and co-vertex (0,−12) .
The equation the requires ellipse is x2169+y2144=1 .
Given information: The focus of the ellipse is (−5,0) and co-vertex is (0,−12) .
Formula used: The equation of the ellipse with vertices (±a,0) and co-vertices (0,±b) is,
x2a2+y2b2=1 ; a>b>0 .
The coordinates of the foci are (±c,0) .
Here, c2=a2−b2 .
Calculation:
Since, focus of the ellipse is (−5,0) then other focus is (5,0) and co-vertex is (0,−12) then other co-vertex is (0,12) .
Then c=5 and b=12 .
Since, c2=a2−b2
This implies that a2=c2+b2 .
Hence,
a2=52+122=25+144=169a=±13
Put a=13 and b=12 in x2a2+y2b2=1 ,
x2132+y2122=1
Therefore, the required equation of the ellipse is x2169+y2144=1 .
Chapter 10 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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