Question

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

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

Answer 1

The correct option is A

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

Given : The equation of the parabola is $y^2-x-2y+2=0$

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

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

$LetX=x-1,Y=y-1$

$\therefore Y^2=X$

Comparing with $Y^2=4aX$

$a=\frac{1}{4}$

$Focus=(X=a,Y=0)=(X=\frac{1}{4},Y=0)$

$=(x=\frac{1}{4},y=1)=(x=\frac{5}{4},y=1)$

Hence,the focus is at $(\frac{5}{4},1)$