The extremities of latus rectum of a parabola are (1, 1) and `(1,-1)` . Then the equation of the parabola can be (a)`y^2=2x-1` (b) `y^2=1-2x` (c)`y^2=2x-3` (d) `y^2=2x-4`

Options

A. `y^(2)+2x-1`
B. `y^(2)=1-2x`
C. `y^(2)=3-2x`
D. `y^(2)=2x-4`

Answer

A, C

Explanation

1,3 Given that the extremities of the latus rectum are (1,1) and (1,-1). Then,
`4a=2ora=(1)/(2)`
Also, the focus of the parabola is (1,0).
Hence, the vertex can be (1/2,0) or (3/2,0).
therefore, the equations of the parabola can be
`y^(2)=2(x-(1)/(2))`
`ory^(2)=-2(x-(3)/(2))`
`i.e., y^(2)=2x-1`
`ory^(2)=3-2x`