Question

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

• A. $\left(\frac{5}{4},1\right)$
• B. $\left(\frac{1}{4},0\right)$
• C. $(1,1)$
• D. none of these

Answer 1

Answer: (A)

$\left(\frac{5}{4},1\right)$

On solving the equation of parabola reduces to form $(y-1{)}^2=(x-1)$
Thus the vertex of parabola is $(1,1)$ and $L.R$ is $1$
Focus will be $(x-1=\frac{1}{4}),y-1=0$
Thus, focus is $\frac{5}{4},1$