document.write( "Question 862560: how to find Find the center, vertices, foci and asymptotes of this equation
\n" ); document.write( " $\"+9x%5E2+-+y%5E2+%2B+18x+%2B+6y+-+4+=+0\"$ \n" ); document.write( "

Algebra.Com's Answer #519828 by josgarithmetic(39620) $\"\"$ $\"About$

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Complete the Squares for the x and the y and adjust to standard form equation. The form possible will tell you which conic section is the equation. \r
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\n" ); document.write( "\n" ); document.write( "That alone is not enough; but you should be able to check your textbook instruction as a reference for more information about foci and asymptotes for the particular conic section you found. The center and vertices are the easy parts.\r
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\n" ); document.write( "\n" ); document.write( "The term for completing the square for the x is 1, as long as first factor the 9 from the terms with x; and the term for completing square for the y is 9, as long as you factor a negative 1 from the terms of y first. You also must use additive inverses to maintain equality.\r
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\n" ); document.write( "\n" ); document.write( "One of the steps will look like this:
\n" ); document.write( " $\"9%28x%5E2%2B2x%2B1%29-%28y%5E2-6y%2B9%29-4-9%2B9=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Further steps should produce this:
\n" ); document.write( " $\"highlight%28%28x%2B1%29%5E2%2F%282%2F3%29%5E2-%28y-3%29%5E2%2F2%5E2=1%29\"$ .
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\n" ); document.write( "HYPERBOLA, centered at (-1,3), vertices at $\"x=-1-2%2F3\"$ and $\"x=-1%2B2%2F3\"$ both with y=3. The a value in reference to standard form, is $\"a=2%2F3\"$ ; and the b value is $\"b=2\"$ . Each focus is a distance c from the center point, and the relationship among a, b, and c is $\"a%5E2%2Bb%5E2=c%5E2\"$ , so you can now find the value of c. \n" ); document.write( "

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