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

Options

A. `(1,(11)/(4))`
B. `(2,(11)/(4))`
C. `(3,(13)/(4))`
D. `(2,(13)/(4))`

Answer

B

Explanation

AC is parallel to y-axis and its mid-point is (2,2). Thus, `B -= (3,2)` and `D -= (1,2)`.
Equation of parabola,
`(x-2)^(2) = lambda (y-3)`
It passes through `(3,2)`, so
`1 =- lambda rArr lambda = -1`
`:. (x-2)^(2) =- (y-3)`
Hence, axis is `x -2 =0, L.R.` line is `y -3 =- (1)/(4)`
`:.` Focus `-= (2,(11)/(4))`