In the given figure, a parabola is drawn to pass through the vertices B, C and D of the square are ABCD .If the coordinates of A and C are  (2,1) and (2,3), respectively, then focus of this parabola is

 

$AC\text{ is parallel to }y\text{ axis, its mid point is }(2,2)\text{ . }$

$\text{ Thus, }B\equiv (3,2)\text{ and }D\equiv (1,2)\text{ . }$

$\text{ Equation of parabola is }(x-2{)}^2=\lambda (y-3)\text{ . }$

$\text{ It passes through }(3,2),\text{ so }\lambda =-1\text{ . }$

$\text{ Thus, equation of parabola reduces to }(x-2{)}^2=-(y-3)\text{ . }$

$\text{ Hence, axis is }(x-2{)}^2\text{ and latus rectum line is }y-3=-1/4\text{ . }$

$\text{ For focus, }x-2=0\text{ and }y-3=-1/4\text{ . }$

$\text{ Therefore, focus is }(2,11/4)\text{ . }$