document.write( "Question 828236: Find the equation of the line parallel to the line x-3y=2 and passing at a distance 2√10 from the given line. \n" ); document.write( "

Algebra.Com's Answer #499165 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
The given line is $\"y=%281%2F3%29x-2%2F3\"$ so any general point of the line is (x,(1/3)(x-2)).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You want another line, $\"y=%281%2F3%29x%2Bb\"$ , to be distance $\"2%2Asqrt%2810%29\"$ from the given line. General point of the wanted line is (x,(1/3)x+b).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Distance Formula:

\n" ); document.write( "and what is needed is a formula for b in terms of x or no terms of x.
\n" ); document.write( "'
\n" ); document.write( " $\"%280%2B%28%281%2F3%29%28x-2%29-%28%281%2F3%29x%2Bb%29%29%5E2%29=4%2A10\"$
\n" ); document.write( " $\"%28x%2F3-2%2F3-x%2F3-b%29%5E2=40\"$
\n" ); document.write( " $\"%28-2%2F3-b%29%5E2=40\"$
\n" ); document.write( " $\"%28b%2B2%2F3%29%5E2=40\"$
\n" ); document.write( " $\"b%2B2%2F3=0%2B-+2%2Asqrt%2810%29\"$
\n" ); document.write( " $\"b=-%282%2F3%29%2B-+2%2Asqrt%2810%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Two possible equations then would be $\"highlight%28y=%281%2F3%29x-%282%2F3%29-2%2Asqrt%2810%29%29\"$ and $\"highlight%28y=%281%2F3%29x-2%2F3%2B2%2Asqrt%2810%29%29\"$ \n" ); document.write( "

\n" );