Question

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

• 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 1

The correct option is B $(y-1{)}^2=8(x-1)$

we have,

$y^2=4ax$

$(y-1{)}^2=4a(x-1)$

$x-1=a,y-1=0$

$\Rightarrow x=a+1,y=1$

now, $S=(a+1,1)$

given,

$Sa+1=3\Rightarrow a=2$

$vs=\sqrt{(3-1{)}^2+(1-1{)}^2}=a=2$

$\Rightarrow (y-1{)}^2=4\times 2(x-1)$

$\therefore (y-1{)}^2=8(x-1)$ is the required equation.