Question

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

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

Answer 1

Answer: (B)

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

GIven equation of parabola $y^2-x-2y+2=0$ can be rewritten in its standard form $(y-k{)}^2=4a(x-h)$ ..... $\left(i\right)$

with centre $(h,k)$

i.e. $(y-1{)}^2=x-1$ ..... $\left(ii\right)$

Comparing with $\left(i\right)$, we get

$h=1,k=1$ and $a=\frac{1}{4}$

Focus of $\left(i\right)$ is given as $(h+a,k)$

Thus, the focus of $\left(ii\right)$ is $(\frac{5}{4},1)$

Hence, option B is correct.