document.write( "Question 911572: Find the points where these conics intersect.\r
\n" ); document.write( "\n" ); document.write( "16𝑥^2 − 5𝑦^2 = 64 and 16𝑥^2 + 25𝑦^2 − 96𝑥 = 256 \n" ); document.write( "

Algebra.Com's Answer #553192 by Fombitz(32388) $\"\"$ $\"About$

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1. $\"16x%5E2-5y%5E2=64\"$
\n" ); document.write( "2. $\"16x%5E2+%2B+25y%5E2-96x+=+256\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"5y%5E2=16x%5E2-64\"$
\n" ); document.write( " $\"25y%5E2=80x%5E2-320\"$
\n" ); document.write( "Substitute into eq. 2,
\n" ); document.write( " $\"16x%5E2+%2B+80x%5E2-320-+96x+=+256\"$
\n" ); document.write( " $\"96x%5E2-96x-320=256\"$
\n" ); document.write( " $\"96x%5E2-96x-576=0\"$
\n" ); document.write( " $\"x%5E2-x-6=0\"$
\n" ); document.write( " $\"%28x-3%29%28x%2B2%29=0\"$
\n" ); document.write( "Two solutions in x:
\n" ); document.write( " $\"x-3=0\"$
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"5y%5E2=16%289%29-64\"$
\n" ); document.write( " $\"5y%5E2=144-64\"$
\n" ); document.write( " $\"5y%5E2=80\"$
\n" ); document.write( " $\"y%5E2=16\"$
\n" ); document.write( " $\"y=4\"$ and $\"y=-4\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"x%2B2=0\"$
\n" ); document.write( " $\"x=-2\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"5y%5E2=16%284%29-64\"$
\n" ); document.write( " $\"5y%5E2=0\"$
\n" ); document.write( " $\"y=0\"$
\n" ); document.write( "So the points are,
\n" ); document.write( "(3,4), (3,-4), and (-2,0) \n" ); document.write( "

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