Question

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

• A. (0,0)
• B. $(\frac{1}{2},\frac{1}{4})$
• C. $(\frac{-1}{4},0)$
• D. $(\frac{-1}{4},\frac{1}{8})$

Answer 1

The correct option is C

$(\frac{-1}{4},0)$

Given: Equation of the parabola y=$2x^2+x$

$\Rightarrow x^2+\frac{x}{2}=\frac{y}{2}$

$\Rightarrow {(x+\frac{1}{4})}^2=\frac{y}{2}+\frac{1}{16}$

$\Rightarrow {(x+\frac{1}{4})}^2=\frac{8y+1}{16}$

$\Rightarrow {(x+\frac{1}{4})}^2=\frac{1}{2}(y+\frac{1}{8})$

$LetX=x+\frac{1}{4},Y=y+\frac{1}{8}$

$\therefore X^2=\frac{1}{2}Y$

Comparing with $X^2=4aY$

$a=\frac{1}{8}$

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

Hence,the focus is at $\frac{-1}{4},0$