Question 951869
a)Write the equation of the parabola in standard form: {{{y^2+6x-4y-9=0}}}

The standard form of a parabola's equation is generally expressed:

{{{y=ax^2+bx+c}}}

so, {{{y^2+6x-4y-9=0}}} will be:

{{{y^2-4y=-6x+9}}}

{{{(y^2-4y+_)-_=-6x+9}}}...complete square

{{{(y^2-4y+2^2)-2^2=-6x+9}}}

{{{(y-2)^2-4=-6x+9}}}

{{{(y-2)^2=-6x+9+4}}}

{{{sqrt((y-2)^2)=sqrt(-6x+13)}}}

{{{y-2=sqrt(-6x+13)}}}

{{{highlight(y=(_+-sqrt(-6x+13))+2)}}}-the equation of the parabola in standard form


{{{ graph( 600, 600, -10, 10, -10, 10,sqrt(-6x+13)+2, -sqrt(-6x+13)+2) }}}


b)Write the equation of the parabola in standard form: {{{y^2+10x+10y-5=0}}}


{{{y^2+10x+10y-5=0}}}

{{{y^2+10y=-10x+5}}}

{{{(y^2+10y+_)-_=-10x+5}}}

{{{(y^2+10y+5^2)-(5^2)=-10x+5}}}

{{{(y+5)^2-25=-10x+5}}}

{{{(y+5)^2=-10x+5+25}}}

{{{sqrt((y+5)^2)=sqrt(-10x+30)}}}

{{{y+5=sqrt(-10x+30)}}}

{{{highlight(y=_+-sqrt(-10x+30)-5)}}}


{{{ graph( 600, 600, -10, 10, -15, 10,sqrt(-10x+30)-5, -sqrt(-10x+30)-5) }}}