document.write( "Question 1180216: Which hyperbolas have one vertex in common with the hyperbola
\n" ); document.write( "(y-4)^2/7^2-(x+6)^2/8^2=1?\r
\n" ); document.write( "\n" ); document.write( "a. (y-8)^2/5^2-(x+6)^2/6^2=1
\n" ); document.write( "b. (x-1)^2/8^2-(y-11)^2/7^2=1
\n" ); document.write( "c. (x+15)^2/9^2-(y+3)^2/5^2=1
\n" ); document.write( "d. (y-6)^2/6^2-(x+6)^2/4^2=1
\n" ); document.write( "e. (y-23)^2/12^2-(x+6)^2/8^2=1
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #809839 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
Which hyperbolas have one vertex in common with the hyperbola\r
\n" ); document.write( "\n" ); document.write( " $\"%28y-4%29%5E2%2F7%5E2-%28x%2B6%29%5E2%2F8%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "Up-down hyperbola with center ( $\"h\"$ , $\"k\"$ )= ( $\"-6\"$ , $\"4\"$ ), $\"a=7\"$ , $\"b=8\"$ \r
\n" ); document.write( "\n" ); document.write( "The vertices: \r
\n" ); document.write( "\n" ); document.write( "( $\"h\"$ , $\"k%2Ba\"$ ), ( $\"h\"$ , $\"k-a\"$ )
\n" ); document.write( "=>( $\"-6\"$ , $\"4%2B7\"$ ), ( $\"-6\"$ , $\"4-7\"$ )
\n" ); document.write( " =>( $\"-6\"$ , $\"+11\"$ ), ( $\"-6\"$ , $\"-3\"$ )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "a.\r
\n" ); document.write( "\n" ); document.write( " $\"+%28y-8%29%5E2%2F5%5E2-%28x%2B6%29%5E2%2F6%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( " center ( $\"h\"$ , $\"k\"$ )= ( $\"-6\"$ , $\"8\"$ ), $\"a=5\"$ , $\"b=5\"$
\n" ); document.write( "The vertices:
\n" ); document.write( "( $\"h\"$ , $\"k%2Ba\"$ ), ( $\"h\"$ , $\"k-a\"$ )
\n" ); document.write( "=>( $\"-6\"$ , $\"8%2B5\"$ ), ( $\"-6\"$ , $\"8-5\"$ )
\n" ); document.write( " =>( $\"-6\"$ , $\"+13\"$ ), ( $\"-6\"$ , $\"3\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%29%5E2%2F8%5E2-%28y-11%29%5E2%2F7%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "Right-left hyperbola with ( $\"h\"$ , $\"+k\"$ )= ( $\"1\"$ , $\"11+\"$ ), $\"a=8\"$ , $\"b=7\"$ \r
\n" ); document.write( "\n" ); document.write( "The vertices
\n" ); document.write( "( $\"h%2Ba\"$ , $\"k+\"$ ), ( $\"h-a\"$ , $\"+k\"$ )
\n" ); document.write( "=>( $\"1%2B8\"$ , $\"11+\"$ ), ( $\"1-8\"$ , $\"+11\"$ )
\n" ); document.write( "=>( $\"9\"$ , $\"11+\"$ ), ( $\"-7\"$ , $\"+11\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "c. \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B15%29%5E2%2F9%5E2-%28y%2B3%29%5E2%2F5%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "Right-left hyperbola with ( $\"h\"$ , $\"+k\"$ )= ( $\"-15\"$ , $\"-3+\"$ ), $\"a=9\"$ , $\"b=5\"$
\n" ); document.write( "The vertices
\n" ); document.write( "( $\"h%2Ba\"$ , $\"k+\"$ ), ( $\"h-a\"$ , $\"+k\"$ )
\n" ); document.write( "=>( $\"-15%2B9\"$ , $\"-3+\"$ ), ( $\"-15-9\"$ , $\"+-3\"$ )
\n" ); document.write( "=>( $\"-6\"$ , $\"-3+\"$ ), ( $\"-24\"$ , $\"+-3\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "d. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28y-6%29%5E2%2F6%5E2-%28x%2B6%29%5E2%2F4%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "Up-down hyperbola with center ( $\"h\"$ , $\"k\"$ )= ( $\"-6\"$ , $\"6\"$ ), $\"a=6\"$ , $\"b=4\"$ \r
\n" ); document.write( "\n" ); document.write( "The vertices:
\n" ); document.write( "( $\"h\"$ , $\"k%2Ba\"$ ), ( $\"h\"$ , $\"k-a\"$ )
\n" ); document.write( "=>( $\"-6\"$ , $\"6%2B6\"$ ), ( $\"-6\"$ , $\"6-6\"$ )
\n" ); document.write( "=>( $\"-6\"$ , $\"+12\"$ ), ( $\"-6\"$ , $\"0\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "e. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28y-23%29%5E2%2F12%5E2-%28x%2B6%29%5E2%2F8%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "Up-down hyperbola with center ( $\"h\"$ , $\"k\"$ )= ( $\"-6\"$ , $\"23\"$ ), $\"a=12\"$ , $\"b=8\"$ \r
\n" ); document.write( "\n" ); document.write( "The vertices:
\n" ); document.write( "( $\"h\"$ , $\"k%2Ba\"$ ), ( $\"h\"$ , $\"k-a\"$ )
\n" ); document.write( "=>( $\"-6\"$ , $\"23%2B12\"$ ), ( $\"-6\"$ , $\"23-12\"$ )
\n" ); document.write( " =>( $\"-6\"$ , $\"+35\"$ ), ( $\"-6\"$ , $\"11\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "hyperbolas which have one vertex in common with the given hyperbola:\r
\n" ); document.write( "\n" ); document.write( "c has =>( $\"-6\"$ , $\"-3+\"$ )
\n" ); document.write( "e has =>( $\"-6\"$ , $\"11\"$ )\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );