Question

The focus of the parabola $y^2-x-2y+2=0$ is

• A. $\left(\frac{1}{4},0\right)$
• B. $(1,2)$
• C. $\left(\frac{3}{4},1\right)$
• D. $\left(\frac{5}{4},1\right)$

Answer 1

Answer: (D)

We have, $y^2-2y=x-2$
or ${\left(y-1\right)}^2=x-1$.
Shifting the origin at $\left(1,1\right)$,
we have $x=X+1$ , $y=Y+1$.
The equation ${\left(y-1\right)}^2=\left(x-1\right)$ reduces to $y^2=X$. This represents a parabola with latus rectum $=1$. Coordinates of the focus w.r.t. new axes are $\left(\frac{1}{4},0\right)$. So, the coordinates of the focus w.r.t. old axes are $\left(\frac{5}{4},1\right)$.