The equation of the parabola with its vertex at (1, 1) and focus at (3, 1) is

Options

A. `(x-3)^(2)=8(y-1)`
B. `(y-1)^(2)=8(x-1)`
C. `(y-1)^(2)=8(x-3)`
D. `(x-1)^(2)=8(y-1)`

Answer

B

Explanation

The vetex and focus of the parabola are (1, 1) and (3, 1) respectively.
Clearly, axis is parallel to x-axis and
Latusrectum = 4 (Distance between vertex and focus)
`rArr" Latusrectum "=4xx2=8`
Also, the vertex is on the left hand side of the focus. So, the parabola opens in the poitive direction of x-axis.
Hence, the equation of the parabola is `(y-1)^(2)=8(x-1)`