document.write( "Question 1018044: Find the vertex and focus and end points of the latus rectum of the parabola 5x^2-5x+7y-4=0 \n" ); document.write( "

Algebra.Com's Answer #634212 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"7y=-5x%5E2%2B5x%2B4\"$
\n" ); document.write( " $\"7y=-5%28x%5E2-x%29%2B4\"$
\n" ); document.write( " $\"7y=-5%28x%5E2-x%2B1%2F4-1%2F4%29%2B4\"$ , completing the square using $\"1%2F4\"$ ;
\n" ); document.write( "which, through a few more steps, will give
\n" ); document.write( "as the standard form, $\"highlight%28y=-%285%2F7%29%28x-1%2F2%29%5E2%2B11%2F28%29\"$
\n" ); document.write( "Telling you that the vertex, being a maximum, is at VERTEX: (1/2, 11/28).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The equation in an equivalent form is also $\"highlight%28%287%2F5%29y=-%28x-1%2F2%29%5E2%2B11%2F20%29\"$ .
\n" ); document.write( "Comparing to $\"4py=-%28x-1%2F2%29%5E2%2B11%2F20\"$ , the value of p is the distance between the FOCUS and the vertex.
\n" ); document.write( "-
\n" ); document.write( " $\"4p=7%2F5\"$
\n" ); document.write( " $\"highlight_green%28p=7%2F20%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The focus, being below the vertex for this example, will have x=1/2 but $\"y=11%2F28-7%2F20=%285%2F5%29%2811%2F28%29-%287%2F7%29%287%2F20%29\"$
\n" ); document.write( " $\"y=%2855-49%29%2F%28140%29\"$
\n" ); document.write( " $\"y=6%2F140\"$
\n" ); document.write( " $\"y=3%2F70\"$
\n" ); document.write( "FOCUS: ( 1/2, 3/70 ).
\n" ); document.write( " \n" ); document.write( "

\n" );