SOLUTION: Identify the type of conic section that has the equation 9x2+ 25y2 =225 and identify its domain and range

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Question 1062630: Identify the type of conic section that has the equation 9x2+ 25y2 =225 and identify its domain and range
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is an ellipse
The general form is:
+x%5E2+%2Fa%5E2+%2B+y%5E2+%2F+b%5E2+=+1+
Multiply both sides by +a%5E2%2Ab%5E2+
+b%5E2%2Ax%5E2+%2B+a%5E2%2Ay%5E2+=+a%5E2%2Ab%5E2+
+3%5E2%2Ax%5E2+%2B+5%5E2%2Ay%5E2+=+5%5E2%2A3%5E2+
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So, in your equation,
+b%5E2+=+9+
+b+=+3+
+b+=+-3+
and
+a%5E2+=+25+
+a+=+5+
+a+=+-5+
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The domain is from +x+=+-a+ to +x+=+a+, which is
x+=++-5+ to +x+=+5+
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The range is from +x+=+-b+ to +x+=+b+, which is
+y+=+-3+ to +y+=+3+
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Hope this helps