$In$ this exercise, $we$ consider parabolas whose axis $of$ symmetry need not $be$ parallel $to$ the $y-$axis.

$(a)$ Find the equation $of$ the parabola with focus $(\frac{1}{4},0)$ and directrix $x=-\frac{1}{4}.$

$(b)$ Find the equation $of$ the parabola with focus $(2,7)$ and directrix $3x+4y=1a{x}^2+bx+c{y}^2+dy+$exy$=f.Lbe$ the line with equation $Ax+By=C,$ and let $(x_0,y_0)a{x}^2+bx+c{y}^2+dy+$exy$=f.$ The constants $a,$dots,$f$ will depend $on$

$\{$:$A,B,C,x_0,y_0.)$