Question

Equation of the parabola with its vertex at $(1,1)$ and focus $(3,1)$ is

• A. $(x-1{)}^2=8(y-1)$
• B. $(y-1{)}^2=8(x-3)$
• C. $(y-1{)}^2=8(x-1)$
• D. $(x-3{)}^2=8(y-1)$

Answer 1

Answer: (C)

As the vertex is $(1,1)$ and focus is $(3,1)$,
whose ordinate is same its axis of symmetry is $y=1$.
And as vertex is equidistant from foci and directrix,
and latter is perpendicular to axis of symmetry.
Directrix is $x=1$
As parabola is the locus of a point whose distance from directrix $x+1=0$ and focus $(3,1)$
Its equation is $(x-3{)}^2+(y-1{)}^2=(x+1{)}^2$
$\Rightarrow x^2-6X+9+y^2-2Y+1=x^2+2X+1$
$\Rightarrow y^2-2y+9=8x$
$\Rightarrow (y-1{)}^2=8(x-1)$